When a proton is removed from point A and an electron is placed at point B, the direction of the electric force will be from point B towards point A. The angle of this force relative to the x-axis would be 180 degrees, with counterclockwise as positive.
As the electron and proton have equal and opposite charges, the magnitude of the force between them will be the same as the magnitude of the force between the proton and the electron.
The magnitude of the force between the proton and electron can be determined by Coulomb's law, which states that the force is proportional to the product of the charges and inversely proportional to the square of the distance between them.
In other words, the magnitude of the two forces is equal, but the direction of the two forces is opposite.
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if a simple pendulum oscillates with small amplitude and its length is doubled, what happens to the frequency of its motion? (a) it doubles. (b) it becomes times as large. (c) it becomes half as large. (d) it becomes 1/ vc times as large. (e) it remains the same.
Option E - it remains the same , if a simple pendulum oscillates with small amplitude and its length is doubled .
The greatest displacement or distance that a point on a wave or vibrating body may travel in relation to its equilibrium position
A wave's amplitude is the difference between its starting position and its maximum displacement. Frequency is the amount of waves which pass past the certain place each second. Period is the length of time it takes for a wave cycle to finish.
Given,length of a simple pendulum is doubled .
To find, frequency of motion.
we have Time period T before doubling the length,
T = 2π[tex]\sqrt{\frac{L}{g} }[/tex] L- length,g-acceleration due to gravity
T/2π = [tex]\sqrt{\frac{L}{g} }[/tex]
g = L(2π/T[tex])^{2}[/tex] → 1
when length is doubled,Time period [tex]T^{'}[/tex]
[tex]T^{'}[/tex] = 2π [tex]\sqrt{\frac{2L}{g} }[/tex]
( [tex]T^{'}[/tex] /2π[tex])^{2}[/tex] = [tex]\frac{2L}{g}[/tex]
g=2L( 2π/T[tex])^{2}[/tex] → 2
from equation 1 and 2
L( 2π/T[tex])^{2}[/tex] = 2L( 2π/T[tex])^{2}[/tex]
2π/T=[tex]\sqrt{2}[/tex](2π/T)
1/T =[tex]\sqrt{2}[/tex](1/T)
we know,frequency γ = 1/T
γ =[tex]\sqrt{2}[/tex] γ '
γ ' =[tex]\frac{1}{\sqrt{2} }[/tex] γ
Therefore option E is correct.
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If the work required to speed a car up from 10km/h to 20km/h is 5.0 x 10^3 J, what would be the work required to increase the cars speed from 20km/h to 30km/h?
If the work required to speed a car up from 10km/h to 20km/h is 5.0 x 10^3 J, the work required to increase the cars speed from 20km/h to 30km/h is: 8.33 × 10³J.
How to find the work required?Using this formula to determine the work required to increase the cars speed from 20km/h to 30km/h
[tex]Wii = Wi (V^2_2- V^2_1) /v^2_2 - v^2_1[/tex]
Let plug in the formula
Work required = (5 × 10³) (30² -20²) / (20² -10²)
Work required = (5 × 10³) ( 900 - 400) /(400 - 100)
Work required = (5 × 10³) ( 500) / 300
Work required = 8.33 × 10³J
Therefore the Work required is 8.33 × 10³J.
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2. A 38kg child is at the top of a slide that is 2. 1m tall.
(a) If there is no friction, how fast will they be moving when they reach the bottom of the slide?
(b) If they lose 250. 0J of energy to sound, heat, and friction, how fast will they be moving when they reach the bottom?
Answer:
3. A 0. 850 kg air-track glider moving at 1. 75 m/s bumps into a 1. 45 kg glider initially at rest.
(a) If the collision is elastic, find the total kinetic energy after collision.
(b) If the collision is completely inelastic, find the total kinetic energy after collision.
Show all your work
Part a: Velocity with no friction: v = 6.41 m/s.
Part b: velocity of the moving object when it reached at the bottom is found as 5.29 m/s.
Explain the term kinetic energy?Kinetic energy, which may be seen in the movement of an item or subatomic particle, is indeed the energy of motion. Kinetic energy is present in every particle and moving object.Potential energy P.E
P.E = mgh
P.E = 38 x 9.8 x 2.1 J
This all transforms to kinetic energy just at bottom = 0.5 mv² if there is no energy loss.
So,
0.5 x 38 x v² = 38 x 9.8 x 2.1,
v = 6.41 m/s
Part b: If friction results in a loss of energy of 250 J
0.5 x 38 x v² = 38 x 9.8 x 2.1 - 250
v² = 532.04/ (0.5 x 38)
v = 5.29 m/s
Thus, the velocity of the moving object when it reached at the bottom is found as 5.29 m/s.
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The correct question is-
2. A 38kg child is at the top of a slide that is 2. 1m tall.
(a) If there is no friction, how fast will they be moving when they reach the bottom of the slide?
(b) If they lose 250. 0J of energy to sound, heat, and friction, how fast will they be moving when they reach the bottom?
Find the distance and displacement of Greyhound bus traveling 90km north and 15km south
here is ur answer
MARK BRAIN PLease
if the distance between atoms in a solid is 175 pm, what velocity must an electron have so that its de broglie wavelength is equal to that distance? what velocity must an ar atom have so that its de broglie wavelength is equal to that distance?
When this problem is solved, we will arrive at the value 72741 to 4 meters per second.
In simple terms, what would you call distance?An object's total, directionless motion is measured in terms of distance. Distance may also be referred to as the amount of ground covered by an element, depending on the starting or finishing point.
Distance calculations' objectiveBy calculating its distance, we can determine an object's actual size. One can measure the space that an object takes up above us. Its true size can be determined after we know how far away it is. As you get further away, something gets smaller.
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How can you differentiate the driver and driven gears in a gear train?
The driver gear is the gear that provides the input motion to the gear train, while the driven gear is the gear that receives motion from the other gears in the train and provides the output motion.
What is driver gear train?This refers to the main or primary gear that majorly drives the other gears found in the gear train.The driver gear is typically connected to a power source, such as an electric motor or a combustion engine, while the driven gear is connected to the load that the gear train is intended to drive. The driver gear is also the one that has the greater torque and the one that rotates faster.
Driven gears refer to the gear that receives motion from the other gears in the train and provides the output motion.
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in a thundercloud there may be electric charges of 35.0 c near the top of the cloud and -35.0 c near the bottom of the cloud. these charges are separated by 2.20 km. what is the electric force on the top charge? magnitude
The magnitude of electric force is [tex]2.27 * 10^{6} N[/tex] (downwards)
We know that electric force between two charges is given by equation:
F = [tex]\frac{k.q_{1} .q_{2} }{r^{2} }[/tex]
Where,
k = constant = [tex]9 * 10^{9} Nm^{2} /C^{2}[/tex]
q1 = first charge =35 C
q2 = second charge = -35 C
r = distance between them = 2.2 km = 2200m
Putting these values in above equation we get:
F = -[tex]2.27 * 10^{6} N[/tex] , where negative sign denotes the direction.
So, the magnitude of electric force is [tex]2.27 * 10^{6} N[/tex] (downwards)
According to Coulomb’s law, the force of attraction or repulsion between two charged bodies is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. It acts along the line joining the two charges considered to be point charges. The law is applicable only for the point charges at rest.To know more about electrostatics visit:
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1. the magnitude (amplitude) of a vibration velocity signal is 0.23 ips at 1170 cpm. find the equivalent displacement amplitude in mils pk-pk and acceleration amplitude in g
In this case, the acceleration amplitude would be (0.23 ips x 1170 cpm)2 = 546.7 g.
What is acceleration?Acceleration is the rate of change of velocity over time. It is a vector quantity, meaning that it has both magnitude and direction. The magnitude of acceleration is the rate at which the velocity changes, and the direction of acceleration is the same as the direction of the velocity.
Displacement amplitude:
The formula for displacement amplitude is displacement amplitude = velocity amplitude / (2πf).
In this case, the displacement amplitude would be 0.23 ips / (2π x 1170 cpm) = 0.00196 inches pk-pk. Converting to mils pk-pk, this would be 1.96 mils pk-pk.
Acceleration amplitude:
The formula for acceleration amplitude is acceleration amplitude = (velocity amplitude x f)2.
In this case, the acceleration amplitude would be (0.23 ips x 1170 cpm)2 = 546.7 g.
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When a potential difference of 125V is applied to two parallel plates, the field between them is 4. 25 x 103N/C. How far apart are the plates?
The distance between the two parallel plates can be found using the equation E = V/d where E is the electric field, V is the potential difference and d is the distance between the plates. Thus, d = V/E = 125V / 4.25 x 103N/C = 29.41cm
What is the relationship between electric field, potential difference, and distance in parallel plates?
The relationship between electric field, potential difference and distance in parallel plates is inversely proportional. As the potential difference increases, the electric field between the plates increases and the distance between the plates decreases. And as the distance between the plates increases, the electric field between the plates decreases and the potential difference applied to the plates decreases.
It can be mathematically represented by the formula E = V / d, where E is the electric field, V is the potential difference, and d is the distance between the plates.
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The distance between the two parallel plates can be found using the equation E = V/d , 29.41cm far apart are the plates .
Evaluating :E = V/d
where E is the electric field,
V is the potential difference and
d is the distance between the plates.
Thus, d = V/E
= 125V / 4.25 x 103N/C
= 29.41cm
Potential difference :The relationship between electric field, potential difference and distance in parallel plates is inversely proportional. As the potential difference increases, the electric field between the plates increases and the distance between the plates decreases. And as the distance between the plates increases, the electric field between the plates decreases and the potential difference applied to the plates decreases.
It can be mathematically represented by the formula E = V / d, where E is the electric field, V is the potential difference, and d is the distance between the plates.
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a race car starts from rest, speeds up with constant acceleration, and reaches a final velocity of 80 m/s. what was the average velocity of the car in m/s?
The average velocity of the car is 40m/s
The average velocity of an object can be determined by dividing the change in position by the change in time.
For this situation, the vehicle begins from rest (initial velocity of 0 m/s) and arrives at a final velocity of 80 m/s.
We can use the equation:
Average velocity = (final velocity + initial velocity) / 2
Average velocity = (80 m/s + 0 m/s) / 2
Average velocity = 40 m/s
This is the average velocity of the vehicle during the entire time interval. Remember that this isn't equivalent to the instantaneous velocity at one point in time, which can be not quite the same as the average velocity.
It's important to take note of that on the off chance that the vehicle's speed increase isn't constant, the average velocity won't rise to the final velocity in addition to the initial velocity isolated by two.
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a ping-pong ball has a diameter of 4.18 cm and average density of 0.0348 g/cm3 . what force would be required to hold it completely submerged under water? the acceleration of gravity is 9.8 m/s 2 . answer in units of n.
The force required to hold the ping pong ball completely under the water is 36,189.98 dyne.
Given:Diameter of ball = 4.18 cm
The radius of the ball = 2.09 cm
The volume of the ball can be calculated as V= [tex]\frac{4}{3}[/tex]π r³
Therefore, the volume of the ball = 38.26 cm³
The net force required to completely submerge a ball under water = (Buoyant force) - (the weight of the ball)
If ρ₁ is used for the density of water. Then, the value of ρ₁ is 1 g cm⁻³.
Buoyant force = ρ₁gV
= 1 × 980 × 38.26
= 37494.80 dyne
Here, ρ₂ = density of ball = 0.0348 1 g cm⁻³.
Weight of ball = ρ₂gV
= 0.0348 × 980 × 38.26
= 1304.82 dyne
Therefore, the net force required to completely submerge a ball under water = 37494.80 - 1304.82 = 36,189.98 dyne or 0.362 N
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you would like to know whether silicon will float in mercury and you know that can determine this based on their densities. unfortunately, you have the density of mercury in units of kilogrammeter3 kilogram meter 3 and the density of silicon in other units: 2.33 2.33 gramcentimeter3 gram centimeter 3 . you decide to convert the density of silicon into units of kilogrammeter3 kilogram meter 3 to perform the comparison. by which combination of conversion factors will you multiply 2.33 2.33 gramcentimeter3 gram centimeter 3 to perform the unit conversion?
The density of silicon is [tex]2.33 * 10^{-9} kg.m^{3}[/tex]
Given density of silicon is 2.33 gram centimeter cube.
We know that:
100 cm = 1 m
1cm = 1/100m = [tex]10^{-2} m[/tex]
[tex]1 cm^{3} = 10^{-6} m^{3}[/tex]
Also,
1000 gram = 1 kg
1 gram = 1/1000 kg = [tex]10^{-3} kg[/tex]
Now, to convert gram centimeter cube into kilogram meter cube we should multiply by these values.
So, By putting these values we get:
Density = 2.33 * [tex]10^{-3} kg * 10^{-6} m^{3} = 2.33 * 10^{-9}kg. m^{3}[/tex]
The density of material shows the denseness of that material in a specific given area. A material’s density is defined as its mass per unit volume. Density is essentially a measurement of how tightly matter is packed together. It is a unique physical property of a particular object. The principle of density was discovered by the Greek scientist Archimedes. It is easy to calculate density if you know the formula and understand the related units The symbol ρ represents density or it can also be represented by the letter D.To know more about density visit:
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How far could a force of 3N pull a wooden block before transferring 12J of energy?
The distance which a force of 3N will pull a wooden block before transferring 12J of energy is 4m.
What is Force?This is referred to as an influence that can change the motion of an object and the unit is Newton.
It has a relationship with distance and work which can be seen below:
Work = Force × distance
12J = 3N × d
d = 12/3 = 4m.
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what is the gauge pressure profile of the water against a section of the container? arrow lengths against the wall indicates pressure magnitude.
Correct Question:
what is the gauge pressure profile of the water against a section of the container?
Gauge pressure is the pressure in relation to atmospheric pressure. For pressures greater than atmospheric pressure, gauge pressure is positive. For pressures lower than atmospheric pressure, gauge pressure is negative.
Pg stands for gauge pressure, which has the following relationships with absolute pressure: pg is equal to p - pa, where Pa is the local atmospheric pressure. Example: The tyre pressure, as determined by a vehicle tyre gauge, is 32.0 psi. The local atmosphere has a pressure of 14.2 psi.
There is pressure between two items that are in touch. The pressure profile is the distribution of pressure throughout the whole contact area.
Since the majority of gauges measure pressure in relation to atmospheric pressure, which acts as the zero point, this form of reading is simply referred to as "gauge pressure." But anything that is not a total vacuum is seen as being under pressure of some kind.
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the building block of all elements and the smallest component into which an element can be divided?
a. building blocks
b. element
c. A molecule
d. atom
The building block of all elements and the smallest component into which an element can be divided d. atom
What is the smallest energy building block?
Quarks, the universe's tiniest particles, are significantly smaller and have far greater energy levels than the protons and neutrons in which they are found.
An atom is the smallest unit of an element that retains all of its characteristics.
However, atoms include several subatomic particles, the most significant of which are protons, neutrons, and electrons.
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at what height above the earth is the acceleration due to gravity 50.0% of its value at the surface?
At the height 2650 km, the value of acceleration due to gravity is 50% of its value at the surface.
The new value of gravity at a height h is given as g' = g R²/(R+h)²
As visible from the formula, increasing h results in decreasing gravity.
So, just put g′ = g/2 i.e. 50% less than g where g is gravity at surface. So, we get,
g/2 = g R²/(R+h)²
1/2 = R²/(R+h)²
2/1 = (R+h)²/R²
√2 = (R+h)/R = 1 + h/R
h/R = √2 - 1 = 0.414
h = 0.414 R
As we know radius of the earth = 6400 km, putting it in the above equation,
h = 0.414 R = 0.414(6400) = 2649.6 km
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A sailor is walking on an aircraft carrier and is observed by a stationary barge. The sailor's velocity according to the barge is 36 m/s. At the same time, the barge observed the aircraft carrier moving at 43 m/s. What is the velocity of the sailor relative to the aircraft carrier?
The velocity of the sailor relative to the aircraft carrier is - 7 m/s.
What is the velocity of the sailor relative to the aircraft carrier?
The velocity of the sailor relative to the aircraft carrier is calculated by applying the principle of relative velocity as shown below.
Vs/c = Vs - Vc
where;
Vs is the velocity of the sailorVc is the velocity of the aircraftThe velocity of the sailor relative to the aircraft carrier is calculated as;
Vs/c = 36 m/s - 43 m/s
Vs/c = -7 m/s
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Joiya grabs a cold bottle of water from the refrigerator and carries it across her dining room. The dining room is at room temperature.
Which of the following describe possible ways heat would be transferred in this system?
The possible ways that heat can be transferred in this system are:
Radiation Conduction How can heat be transferred in this system ?The most typical method of heat transfer is conduction, which involves the direct exchange of heat between two things.
Heat waves are created during the radiation heat transfer process and may be absorbed, reflected, or transmitted through a cooler substance. Earth is warmed by the sun using electromagnetic radiation. Heat waves come from warm bodies.
When Joiya sets the bottle of water down on a table or chair, then by conduction, heat ( or the loss of it ) would move around the table. Radiation would allow for the cold temperature to move into the air around the cold bottle.
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Options for this question include:
Convection Conduction Radiationidentify the main period of motion for a machine operating (and vibrating) at a rotational speed of 1780 cpm in units of seconds.
0.034 second is the main time period of the motion for a machine which is operating at a speed of 1780 cpm.
Time period of an object is the time required for it to complete its one cycle or oscillation. Angular frequency is angular displacement of any object of the waves per unit time. The formula for time is, T = 1/f
where T is time-period and f is frequency.
Operating speed of the machine = 1780 cpm (cycle per minute)
Cycle in one minute = 1780
Cycle in 1 second = 1780/60 = 29.67 cycles
Time required in one cylcle, T = 1/29.67 = 0.034 second
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What is upper fixed
point? How can it be measured explain with figure
The upper fixed point, also known as steam point, is the temperature at which pure water boils at normal atmospheric pressure.
In case of the Celsius scale, the upper fixed point is 100°C.
This is the boiling point of pure water at 1atm which is the normal atmospheric pressure.
What is atmospheric pressure?The pressure that the atmosphere exerts on the earth's surface is called atmospheric pressure.
What is boiling point?The temperature at which liquid water starts changing into vapour is called boiling point.
What is Celcius?Celcius is an unit of measuring temperature.
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in what direction is the force of air friction several seconds after the package has been dropped but before it reaches terminal velocity or hits the ground?
After a brief period of falling, the upward air friction on the cargo would equal the downward gravity pull if a parachute opened.
What forces are at work on something falling at its speed of descent?Air resistance reaches its maximum magnitude at the falling object's terminal velocity. Due to the fact that the two forces are acting in opposing directions, there is no net force acting on the item, and its speed has stabilised.
How do forces act on a dropped object as it is falling?In addition, gravity is pulling the thing downward as it falls. Gravity is an imbalanced force at the beginning of a descent. The result is an increase in speed or acceleration for the object. Aerodynamic drag or air resistance is encountered as it accelerates.
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At a cost of 9. 0 cents/kWh, estimate how much this would add to your monthly electric energy bill if you made toast four mornings per week (16 times per month)
The cost of making toast 16 times per month at a rate of 9.0 cents/kWh is approximately $0.1 per month.
How does the energy consumption of a device change with the length of usage?
The strength consumption of a tool commonly will increase with the duration of utilization. This is due to the fact maximum devices devour electricity continuously at the same time as in use, no matter how long they're used for. Some gadgets, along with appliances with standby or sleep modes, may devour less strength while now not in use, but will eat extra strength the longer they're used. For example, a fridge will consume extra power over a month than it will over an afternoon, and a pc will devour more energy over a 12 months than it's going to over a month.
A few gadgets, consisting of incandescent light bulbs, will eat extra energy and put on out faster the greater they may be used.
We convert from Watt to kilowatt
650/1000 = 0.65KW
We convert from minutes to hour:
6/60= 0.1 hr
Convert cents to dollars
9/100 = $0.09
Energy cost in KWh= 0.65 × 0.1 × 0.09 ×16= $ 0.1 per month
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A roller coaster features a near vertical drop of 150 meters. If the initial velocity was zero, the mass of the cart and riders was 2,000 kg, and the velocity at the end of the drop was 50 m/s, how much of the potential energy was converted into thermal energy?
The amount of the potential energy that was converted into thermal energy is determined as 440,000 J.
What is the potential energy lost to thermal energy?
The amount of the potential energy that was converted into thermal energy is calculated by applying the principle of conservation of energy as follows;
P.E - K.E = Eth
where;
P.E is the potential energyK.E is the kinetic energyEth is the thermal energy( 2,000 kg x 9.8 m/s² x 150 m ) - ¹/₂ (2,000 kg )( 50 m/s )² = Eth
2,940,000 J - 2,500,000 J = Eth
440,000 J = Eth
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how many times more intense is the least intense perceptible sound at 100 hz compared to the least intense perceptible sound at 1000 hz ? specifically, you are looking for the ratio i100hz/i1000hz .
The ratio i100hz/i1000hz is 1000, meaning that the least intense perceptible sound at 100 Hz is 1000 times more intense than the least intense perceptible sound at 1000 Hz.
What is intense?Intense is an adjective describing something that is extreme or powerful, either in terms of strength, emotion, or concentration. It can refer to a feeling, such as intense emotion, or a physical sensation, such as intense pain.
The least intense perceptible sound at 100 Hz is about one millionth of a Pascal, while the least intense perceptible sound at 1000 Hz is about one billionth of a Pascal. Therefore, the ratio i100hz/i1000hz is 1000, meaning that the least intense perceptible sound at 100 Hz is 1000 times more intense than the least intense perceptible sound at 1000 Hz.
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if these objects roll without slipping down a ramp, which one will reach the bottom of the ramp first? multiplechoice : 1) there is not enough information to determine 2) object b 3) object a 4) they will reach the bottom at the same time.
There is not enough information to determine which object will reach the bottom of the ramp first. So option 1 is correct.
Without knowing the mass, radius, and coefficient of friction of the objects and the angle of the ramp, we can't determine which object will have the greater acceleration and thus reach the bottom of the ramp first.
To determine which object will reach the bottom of the ramp first, we need to know the acceleration of each object. The acceleration of an object is determined by the net force acting on it.
Which in turn is determined by the gravitational force acting on the object and the frictional force acting on it.
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a metal object is suspended from a spring scale. the scale reads 936 n when the object is suspended in air, and 769 n when the object is completely submerged in water. find the volume of the object. the acceleration of gravity is 9.8 m/s 2 . answer in units of m3 .
The volume of object will be equal to the volume of water displaced so the object's volume is also 17.04 dm⁻³.
What is volume?In water, the object appears lighter than in air.
That is,
936 - 769 = 167N.
Water provided the167N buoyant force.
The buoyant force on an object in water is equal to the weight of water displaced by the object. The buoyant force acting on the metal object in this case is 167N. The object must have displaced the same weight of water.
Given g = 9.8m/s²
Water displacement mass:
Mass = weight /g
= 167/9.8
. = 17.04 kg
Water displacement volume:
At room temperature, the density of water is 1.000 kg.dm⁻³. Each kilogram of water has a volume of 1 dm³ (one cubic decimeter), which is equal to 1 L. (one liter).
V = Mass / Density
= m/ρ
= 17.04/1.000 kg.dm⁻³
= 17.04dm⁻³
The object is completely submerged. As a result, the object's volume will remain constant. The object is completely submerged. As a result, the object's volume will be equal to the volume of water displaced. The object's volume is also 17.04 dm⁻³.
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which method of naming/locating stars will be the best for giving someone the location of the star?
Celestial navigation is the best method of naming or locating stars, if we have to give someone the location of a star.
With the help of "sights" or time angular measurements taken typically between a celestial body (e.g. the Sun, a planet, the moon or a star) and the visible horizon, Celestial navigation locate a star or any celestial body. However it can also take advantage of measurements between celestial bodies without taking the Earth horizon as reference, such as when the Moon is used in the practice, then it is called "lunars" or lunar distance method, which is used for determining precise time when time is unknown.
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(c) what is the minimum thickness of a soap bubble film (air-soap-air) with refractive index 1.38 that results in a constructive interference in the reflected light if this film is illuminated by a beam of light of wavelength 610 nm?
The minimum thickness of a soap bubble film (air-soap-air) with refractive index 1.38 that results in a constructive interference in the reflected light if this film is illuminated by a beam of light of wavelength 610 nm is 150
nm.
What is refractive index ?The refractive index of an optical medium is described as a dimensionless number that gives the indication of the light bending ability of that medium.
Condition for constructive interference is given as ,
2μt = (2n + 1) λ/2
t = (2n + 1) x 900 / 4x 1.5
where n = 0(for minimum thickness)
Therefore t= 150nm
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five equal forces of 10 N are applied at
a point. If the angle between them is
equal, what is the resultant force?
The resultant force is approximately 11.75 N
solving for the resultant force:If five equal forces of 10 N are applied at a point, and the angle between them is equal, then the forces can be considered as forming a regular pentagon.
The angle between any two adjacent forces in a regular pentagon:
180 - 360 degrees
n
where,
n = the number of sides.
In this case, the angle is
180 - 360
5
θ = 108 degrees.
To calculate the resultant force, we can use vector addition. Since the forces are equal and the angle between them is 108 degrees, we can use the law of cosines to find the magnitude of the resultant force. The law of cosines states that the square of the magnitude of the resultant force (R) is equal to the sum of the squares of the individual forces (F) plus twice the product of the individual forces and the cosine of the angle between them (θ).
R² = F² + F² + 2 * (F) *(F)* cos(108)
R² = 10² + 10² + 2(10)(10)cos(108)
R² = 100 + 100 + 200 * (cos(108))
R² = 100 + 100 + 200 * (-0.309016994)
R = ([tex]\sqrt({100 +100 - 62)}[/tex]
R = √138
R = 11.75 N
The magnitude of the resultant force is approximately 11.75 N, which is the force that would be required to replace all five forces.
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an experimental rocket designed to land upright falls freely from a height of 2.98 102 m, starting at rest. at a height of 96.5 m, the rocket's engines start and provide constant upward acceleration until the rocket lands. what acceleration is required if the speed on touchdown is to be zero? (neglect air resistance.)
The required acceleration has a magnitude of 19.7 m/s2 directed upwards, correct to three significant figures.
The the purpose of analysis, the motion of rocket is divided into two phases.
Phase 1: the free fall motion of the rocket from the height 2.98*102m to a height 96.5m.
Phase 2: the motion of the rocket due to the acceleration of the rocket also from the height 96.5 m to the point of touchdown y = 0m.
The initial velocity of the rocket is 0m/s when it started to experience a fall from rest under free fall. g = 9.8m/s² t1 is the time taken for phase 1 and t2 is the time taken for phase2.
The final velocity under free fall becomes the initial velocity for the accelerated motion of the rocket in phase 2 and the final velocity or speed in phase 2 is equal to zero.
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