The magnitude of the normal force of the car is given by Fn = Fg cotθ.
What is the normal force of the car?The normal force is the force exerted by the racetrack perpendicular to the car's motion. Let's now derive the expression for the magnitude of the normal force of the car:
The perpendicular component of the normal force is given by:
Fn⊥ = Fg cosθ
The parallel component of the normal force provides the centripetal force required for circular motion.
The centripetal force (Fc) is given by:
Fc = mv²/r
where;
m is the mass of the car, v is the velocity of the car, and r is the radius of the circular path.The centripetal force can also be expressed in terms of the parallel component of the normal force:
Fc = Fn∥ = Fn sinθ
Equating the two expressions for Fc, we get:
Fn sinθ = mv²/r
Solving for Fn, we get:
Fn = mv²/(r sinθ)
Substituting the expression for Fg cosθ, we get:
Fn = Fg cosθ / sinθ
or
Fn = Fg cotθ
where;
Fg is the gravitational force, g is the acceleration due to gravity, θ is the angle of banking of the track, and r and v are the radius and velocity of the car respectively.Learn more about normal force here: https://brainly.com/question/14486416
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The complete question is below:
Circular turns of radius r in a racetrack are often banked at an angle θ to allow the cars to achieve higher speeds around the turns. Assume friction is not present.
Now write the magnitude of the normal force of the car, in terms of the gravitational force Fg, g, θ, the radius of the track r, and the velocity that the car is traveling v.
An astronaut floating in space is motionless. The astronaut throws a wrench in one direction, propelling her in the opposite direction. Which of the following statements are true? (Choose all that apply.)
The impulse applied to the wrench is equal and opposite to the impulse applied to the astronaut.
What exactly does velocity mean?
The speed at which a body or object is moving determines its direction of motion. Most of the time, speed is a scalar quantity. In essence, velocity is a vector quantity. The rate at which distance changes is what it is. It is the rate at which displacement is changing.
I. The velocities will not be same
II. Initial momentum = final momentum
0 = Momentum of Astronaut + Momentum of Wrench
Momentum of Astronaut = - Momentum of Wrench
so equal and opposite
this statement is correct.
III. Impulse = change in momentum
As momentum is equal and opposite impulse will also be equal and opposite.
This statement is also correct.
the impulse applied to the wrench is equal and opposite to the impulse applied to the astronaut.
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calculate the energy needed to raise the temperature of 0.40kg of water in an aluminium container of mass 0.20kg from 15 degrees to 40 degrees
aluminium shc - 900 j/kg
Answer:
To calculate the energy needed to raise the temperature of the water, we can use the following formula:
Q = m * c * ΔT
where:
Q = energy (in joules)
m = mass (in kilograms)
c = specific heat capacity (in joules per kilogram per degree Celsius)
ΔT = change in temperature (in degrees Celsius)
We are given:
m of water = 0.40 kg
ΔT = (40 - 15) = 25 °C
m of container = 0.20 kg
c of aluminum = 900 J/kg°C
First, we need to calculate the energy needed to raise the temperature of the container:
Q1 = m1 * c1 * ΔT
Q1 = 0.20 kg * 900 J/kg°C * 25 °C
Q1 = 4500 J
Next, we need to calculate the energy needed to raise the temperature of the water:
Q2 = m2 * c2 * ΔT
Q2 = 0.40 kg * 4186 J/kg°C * 25 °C
Q2 = 41860 J
The total energy needed is the sum of Q1 and Q2:
Q = Q1 + Q2
Q = 4500 J + 41860 J
Q = 46360 J
Therefore, the energy needed to raise the temperature of 0.40 kg of water in an aluminium container of mass 0.20 kg from 15 degrees to 40 degrees is 46360 J.
Explanation:
A box of mass 32.0 kg slides to the right across a horizontal surface with a coefficient of kinetic friction 0.50 while being pulled horizontally by a 750.0 N force. What is the acceleration of the box? Make sure your answer is in MKS units.
The acceleration of the box when pulled horizontally by a 750.0 N force is a = 2.4 m/s2
The acceleration of the box can be calculated by using the equationa = (F - (μk*M*g))/M,
where
F is the force pulling the box,
μk is the coefficient of kinetic friction,
M is the mass of the box, and
g is the acceleration due to gravity.
In this case,
F = 750N,
μk = 0.50,
M = 32.0 kg, and
g = 9.81 m/s2.
Therefore, the acceleration of the box can be calculated as follows:
a = (750N - (0.50*32.0 kg*9.81 m/s2))/32.0 kg = 2.4 m/s2.
The equation used to calculate the acceleration of the box takes into account the force pulling the box and the frictional force acting against it. The frictional force is determined by the coefficient of kinetic friction, which is a measure of the resistance to motion between two surfaces, and the mass of the box.
The acceleration of the box is also affected by gravity, which is why the acceleration due to gravity is included in the equation. Knowing the force and friction acting on the box, we can calculate the acceleration of the box.
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The mass of the moon is 7.35 × 1022 kg and the mass of the earth is 5.98 × 1024 kg. The average distance between the moon and the earth is 3.84 × 108 m. What is this satelite's speed, in km/s (kilometer per second)? Use G = 6.67 × 10-11 N·m2/kg2.
The speed of the moon is approximately 4.70 km/s.
What is the formula to calculate the gravitational force between two objects?The formula to calculate the gravitational force between two objects is F = G * (m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.
How does the distance between two objects affect the gravitational force between them?The gravitational force between two objects is inversely proportional to the square of the distance between them. This means that as the distance between two objects increases, the gravitational force between them decreases. Conversely, as the distance between two objects decreases, the gravitational force between them increases.
We can use the formula for gravitational force to find the speed of the moon:
F = ma = GMm/r^2
where F is the gravitational force between the moon and the earth, m is the mass of the moon, M is the mass of the earth, r is the distance between them, G is the gravitational constant, and a is the acceleration of the moon.
Solving for a, we get:
a = GM/r^2
Using the given values and converting to km and s units:
a = (6.67 × 10^-11 N·m^2/kg^2) × (5.98 × 10^24 kg) / (3.84 × 10^8 m)^2 = 1.99 × 10^-3 m/s^2
Then, we can use the formula for speed (v) and time (t):
v = at
The time it takes for the moon to orbit the earth once is approximately 27.3 days, or 2.36 × 10^6 s. So, we have:
v = (1.99 × 10^-3 m/s^2) × (2.36 × 10^6 s) = 4.70 × 10^3 m/s
Converting to km/s:
v = 4.70 × 10^3 m/s ÷ 1000 = 4.70 km/s
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Write a hypothesis about the pH level of common household solutions based on what you know about their physical and chemical properties. Use the format of "if . . . then . . . because . . .” and be sure to answer the lesson question "How is pH used to determine if a solution is acidic or basic?
The terms "IF" and "THEN" are frequently used when writing the hypothesis. For instance, "I will not pass the test if I don't study." Your variables are reflected in the "if" and "then" lines. A solution is said to be acidic or basic depending on its pH value, which ranges from 7 to 14.
How are acids and bases classified using pH?All compounds fall into one of three categories: basic (pH higher than 7), acid (pH or less 7), or neutral (pH about 7). The pH also indicates how powerful or weak the substance is. For instance, an item with a pH of 8 acts as a weak base, whereas an item with a pH of 3 is a powerful acid.
What is the theory behind the experiment in problem solving?The hypothesis is essentially a prediction of what you believe will occur if you adopt a specific course of action to address an issue. The hypothesis often specifies what will change, what might result from the action, and why you believe the change is necessary.
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The critical fields at 6k at 8k for an alloy are 7.616 & 4.284 Wb/m² resp. Determine the transition temperature and critical field at 0 k temperature?
Answer:
The transition temperature is 0.920 K and the critical field at 0 K is 8.956 Wb/m².
Explanation:
To determine the transition temperature and critical field at 0 K, we need to use the following formula:
Bc(T) = Bc(0)[1-(T/Tc)^2]
where:
Bc(T) = critical magnetic field at temperature T
Bc(0) = critical magnetic field at 0 K
T = temperature
Tc = transition temperature
We have the critical fields at 6 K and 8 K:
Bc(6 K) = 7.616 Wb/m²
Bc(8 K) = 4.284 Wb/m²
We can use these values to find the transition temperature:
7.616 = Bc(0)[1-(6/Tc)^2]
4.284 = Bc(0)[1-(8/Tc)^2]
Dividing the two equations, we get:
7.616/4.284 = [1-(6/Tc)^2]/[1-(8/Tc)^2]
Simplifying the right-hand side:
7.616/4.284 = [(8/Tc)^2 - 1]/[(6/Tc)^2 - 1]
Let x = (8/Tc)^2
Then (6/Tc)^2 = x/64
Substituting into the equation above:
7.616/4.284 = (x - 1)/(x/64 - 1)
Simplifying:
7.616/4.284 = 64(x - 1)/(x - 64)
Multiplying both sides by (x - 64):
7.616/4.284 * (x - 64) = 64(x - 1)
Simplifying:
(x - 64)/(x - 1) = 7.616/4.284 * 1/64
Multiplying both sides by (x - 1):
x - 64 = 7.616/4.284 * 1/64 * (x - 1)
Simplifying:
x = 74.14
Substituting back into (8/Tc)^2 = x:
(8/Tc)^2 = 74.14
8/Tc = ±8.607
Tc = 0.920 K or 0.103 K
Since the transition temperature should be higher than the critical field at 0 K, we choose Tc = 0.920 K.
Now we can use either of the equations for Bc(T) to find Bc(0):
7.616 = Bc(0)[1-(6/0.920)^2]
Bc(0) = 8.956 Wb/m²
Therefore, the transition temperature is 0.920 K and the critical field at 0 K is 8.956 Wb/m².
consider a man of mass 80kg standing 10m from a woman with a mass of 65 kg the attractive gravitational force between them would be ?
please I need a fast verified answer
3.17 x 10^-8 Newtons is the required gravitational force between them.
Determining the gravitational force between objectsThe gravitational force between two objects is given by the formula:
F = G * (m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (6.6743 x 10^-11 N*m^2/kg^2), m1 and m2 are the masses of the two objects, and r is the distance between the centers of mass of the two objects.
In this case, the masses of the man and the woman are:
m1 = 80 kg
m2 = 65 kg
The distance between them is:
r = 10 m
Plugging these values into the formula, we get:
F = 6.6743 x 10^-11 * (80 kg * 65 kg) / (10 m)^2
F = 3.17 x 10^-8 Newtons
Therefore, the attractive gravitational force between the man and the woman is approximately 3.17 x 10^-8 Newtons.
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An object moves from position x = -1.88 m to x = -4.27 m. What is it's displacement?
Answer: Displacement = -2.39 m
Explanation: The displacement of an object is the difference between its final position and its initial position. In this case, the object moved from x = -1.88 m to x = -4.27 m, so its displacement is:
Displacement = Final position - Initial position
Displacement = (-4.27 m) - (-1.88 m)
Displacement = -4.27 m + 1.88 m
Displacement = -2.39 m
Therefore, the displacement of the object is -2.39 m.
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A washbasin has an exit pipe covered with a play of area 12cm². A chain is attached to the centre of the plug to assist in pulling the plag away from the out hole. The washbasin contains water to a depth of 0.08% -3 The density of water is 1000 kgm.
Answer:
To solve this problem, we need to use the principles of fluid mechanics, specifically Bernoulli's equation, which relates the pressure, velocity, and height of a fluid at different points in a system.
First, we need to find the weight of the water in the washbasin. The volume of water is equal to the area of the base of the basin (assuming it's circular) multiplied by the depth of the water:
V = πr²h
where r is the radius of the basin and h is the depth of the water. Since the depth of the water is given as 0.03m, we need to convert it to meters:
h = 0.03 m
The radius of the basin is not given, so we can't calculate the volume directly. However, we can use the fact that the density of water is 1000 kg/m³ to find the weight of the water:
density = mass/volume
mass = density x volume
The mass of the water is then:
m = density x V
Next, we need to find the pressure at the bottom of the basin, which is equal to the weight of the water divided by the area of the base of the basin:
pressure = weight/area
We can then use Bernoulli's equation to relate the pressure at the bottom of the basin to the pressure at the exit pipe:
pressure + 1/2(density)(velocity²) + density(g)(height) = constant
where velocity is the speed of the water flowing out of the pipe, g is the acceleration due to gravity, and height is the height of the water above the exit pipe.
At the bottom of the basin, the velocity of the water is zero, so the second term on the left-hand side of the equation is zero. Also, since the exit pipe is at the same level as the bottom of the basin, the height term is also zero. Therefore, the equation simplifies to:
pressure = constant
which means that the pressure at the exit pipe is equal to the pressure at the bottom of the basin.
Now we can use the pressure at the bottom of the basin and the area of the exit pipe to find the force required to lift the plug:
force = pressure x area
Finally, we need to convert the force to the weight of the plug, which is given by:
weight = force/g
where g is the acceleration due to gravity.
Putting all of these steps together, we get:
V = πr²h = π(0.06m)²(0.03m) = 3.4 x 10⁻⁴ m³
m = density x V = 1000 kg/m³ x 3.4 x 10⁻⁴ m³ = 0.34 kg
pressure = weight/area = m(g)/area = (0.34 kg)(9.8 m/s²)/(12 x 10⁻⁴ m²) = 2.8 x 10³ Pa
force = pressure x area = (2.8 x 10³ Pa)(12 x 10⁻⁴ m²) = 0.34 N
weight = force/g = 0.34 N/9.8 m/s² = 0.034 kg
Therefore, the weight of the plug is 0.034 kg, or approximately 34 grams.
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An object of mass 50 g is attached to a string of length 50 cm which will break if tension is 20 N. The object is whirled in a vertical circle, the axis of rotation being at a height of 100 cm above the ground. The angular speed is very slowly increased until the string breaks. In what position is the week is likely to occur and of what angular speed? Where will the object hits the ground?
Answer:
sorry hindi q po alm hahahahahah
Aluminum
13
AI
26.982
Answer:
Aluminum is a chemical element with the symbol Al and atomic number 13. Its atomic weight is approximately 26.982 u.
Explanation:
State ar Chinese’s principle
Answer:
The three principles are often translated into and summarized as nationalism, democracy, and the livelihood of the people.
A truck covers 40.0 m in 9.15 s while uniformly slowing down to a final velocity of 2.20 m/s.
(b) Find its acceleration.
Incorrect: Your answer is incorrect.
m/s2
Answer:
0.24ms^-2
Explanation:
a=v/t2-t1
a =2.24/9.15
a= 0.24 m/s^-2
What is electrical energy?
A. The ability to do work.
B. The energy of moving electrons.
C. The energy of electricity.
D. The force of moving atoms.
Answer:
The answer is A( The ability to do work)
or B it's in between those two answers
The diagram below shows three kettles with their powers and the time they take to boil 500cm3 of water. If electricity costs 9p per unit, how much does it cost to boil 500cm3 of water using the 1.4kW kettle?
NOTE IF YOU ARE RIGHT YOU WILL GET A BRAINLY!!
The cost of boiling 500 cm³ of water using 1.4kW kettle is 0.945 p
How do I determine the cost of boiling water using 1.4 KW kettle?We shall begin our calculation by obtaining the energy consumed when using 1.4 KW kettle. This is shown below:
Power (P) = 1.4 KW Time (t) = 4.5 minutes = 4.5 / 60 = 0.075 hoursEnergy (E) =?E = Pt
E = 1.4 × 0.075
E = 0.105 KWh
Finally, we shall determine the cost of boiling the water using the 1.4 KW kettle. Details below
Cost per KWh = 9 pEnergy (E) = 0.105 KWhCost of boiling =?Cost = energy × Cost per KWh
Cost of boiling = 0.105 × 9
Cost of boiling = 0.945 p
Thus, we can conclude that the cost of boiling is 0.945 p
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Draw a ray diagram to locate an image formed by a lens when a object is placed at 2f
The ray diagram of the lens at 2f is shown in the image attached.
What is a ray diagram?
A ray diagram is a diagram used to illustrate the behavior of light as it travels through a system of optical components such as lenses, mirrors, or prisms. The diagram shows the path of light rays from an object, through the optical system, to form an image.
Ray diagrams are commonly used in optics to predict the behavior of light and to design optical systems for various applications, such as telescopes, microscopes, cameras, and eyeglasses.
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Challenge: Draw a complex circuit. This circuit should have four light bulbs (two in parallel and
two in series), two switches (one to turn off series lights and one to turn off parallel lights), and
one battery.
The circuit would have one battery with a positive and negative terminal. Connected to the positive terminal would be one switch and then two light bulbs in series. The other end of the two light bulbs in series would be connected to the negative terminal of the battery. Connected in parallel to the two light bulbs in series would be another two light bulbs. The positive end of the first parallel light bulb would be connected to the positive end of the second parallel light bulb. The other ends of both parallel light bulbs would be connected to the negative terminal of the battery. The first switch would be connected to the two light bulbs in series and would turn off only those two light bulbs when switched. The second switch would be connected to the two light bulbs in parallel and would turn off only those two light bulbs when switched.
What is a series connection?In electronics, a series connection refers to a circuit in which the components (such as resistors, capacitors, or light bulbs) are connected end-to-end in a single path, so that the same current flows through each component in turn.
In a series connection, the voltage applied to the circuit is divided among the components according to their individual resistance or impedance values. The total resistance of a series circuit is equal to the sum of the individual resistances of each component.
In a series connection, the total voltage across the circuit is equal to the sum of the individual voltage drops across each component.
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Compare the slant range Ri and flight time ti for the depicted projectile with the range R and flight time t for a projectile (launched with speed v0 and inclination angle α) which flies over a horizontal surface. Evaluate your four results for v0 = 80m/s and α = 16°
The slant range and flight time for the projectile in the illustration are roughly Ri = 1013.7 m and ti = 12.4 s for v0 = 80 m/s and = 16°. R = 921.8 m and t = 9.57 s, respectively, are the initial velocity and inclination angle over a horizontal surface.
Describe a projectile.Any item launched into space with just gravity acting on it is referred to as a projectile. Gravity is the main force affecting a projectile.
Considering that the projectile's initial speed is 80 m/s and its inclination towards the horizontal is 16 degrees,
Range R: R = ([tex]v0^2/g[/tex]) * sin(2α)
Flight time t: t = (2 * v0 * sinα) / g
Plugging in the given values, we get:
Range R: R = ([tex]80^2/9.81[/tex]) * sin(2*16°) ≈ 921.8 m
Flight time t: t = (2 * 80 * sin16°) / 9.81 ≈ 9.57 s
To calculate the slant range and flight time for the depicted projectile, we can use the following equations:
Slant range Ri: Ri = √([tex]H^2 + R^2[/tex]), where H is the height of the elevated position
Flight time ti: ti = (2 * v0 * sinα + √([tex]4 * v0^2 * sin^2α + 8 * H * g[/tex])) / (2 * g)
From the diagram, it appears that the elevated position is approximately 150 meters above the ground, so we can use H = 150m in our calculations:
Slant range Ri: Ri = √([tex]150^2 + 921.8^2[/tex]) ≈ 1013.7 m
Flight time ti: ti = (2 * 80 * sin16° + √([tex]4 * 80^2 * sin^2[/tex](16°) + 8 * 150 * 9.81)) / (2 * 9.81) ≈ 12.4 s.
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What is the Mass of a 80 n dog
Answer:
80 n
Explanation:
Which of the following ideas provided an important step towards a more complete understanding of blackbody radiation
The following theories contributed significantly to a more full knowledge of black body radiation. Light is made up of separate pieces that must be absorbed together.
What is the cause of black body radiation?A black body is an object that absorbed all radiation falling on it at all wavelengths. When a black body is at a constant temperature, its emission exhibits a temperature-dependent frequency distribution. It emits what is known as black-body radiation.
What exactly is the black body radiation experiment?One of the first experiments that led to quantum mechanics was blackbody radiation. It all started with the basic observation that when you heat a metal, it first turns red, then yellow, and finally white hot as the temperature rises.
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If a central air conditioner (at its highest wattage) runs for 8 hours, how much energy is used?
A)4 kwh
B)8 kwh
C) 32 kwh
D)60 kwh
The central air conditioner's energy consumption while it operates at its maximum wattage for 8 hours: 40 kWh.
If a central air conditioner (at its highest wattage) runs for 8 hours, how much energy is used?We need to know the air conditioner's power usage in watts (W) and how long it runs for in hours in order to determine the energy it consumes (h). Calculating energy usage uses the following formula:
Power (W) x Time (h) / 1000 = Energy (kWh)
We can determine the energy usage as follows if we assume that the air conditioner uses 5000 watts (5 kW) of power at its peak wattage for 8 hours:
Power (W) x Time (h) / 1000 = Energy (kWh)
Energy (kWh) = 5000 W x 8 hours / 1,000
Energy is equal to 40 kWh.
Consequently, choice D corresponds to the central air conditioner's energy consumption while it operates at its maximum wattage for 8 hours: 40 kWh.
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A 230 g air track glider is connected to a string hanging over a frictionless pulley. A 100g mass hangs from the other end of the string. Find the acceleration of each.
Answer:
a= 2.97m/s²
Explanation: mg = (M+m)a, with M the mass of the g
a= 100(230+100)g .
define power of a lens. the focal length of a lens is -10 cm. write the nature of the lens and find its power. if an object is placed at a distance of 20cm from the optical centre of this lens, according to the New Cartesian Sign Convention, what will be the sign of magnification in this case
The power of a lens is the degree to which it can converge or diverge light rays and is expressed in dioptres (D).
Lens explained.
The power of a lens is the degree to which it can converge or diverge light rays and is expressed in dioptres (D). It is defined as the reciprocal of the focal length of the lens in meters.
Given that the focal length of the lens is -10 cm, we can convert it to meters by dividing it by 100:
f = -10 cm = -0.1 m
The negative sign indicates that the lens is a diverging lens, also known as a concave lens.
To find the power of the lens:
P = 1/f = 1/(-0.1 m) = -10 D
Therefore, the power of the lens is -10 dioptres.
If an object is placed at a distance of 20 cm from the optical centre of this lens, according to the New Cartesian Sign Convention, the object distance is positive (u = 20 cm). Since the lens is a diverging lens, the image formed will be virtual, erect and smaller than the object. The image distance will be negative (v < 0).
Using the formula for magnification:
m = -v/u
We get:
m = -(-10 cm) / (20 cm) = 0.5
Therefore, the negative sign indicates that the image is inverted, but since it is a virtual image, we say it is erect. The magnitude of magnification is less than 1, which means the image is smaller than the object.
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We build a mount with a convergent lens and an object of size 3 cm and we obtain on a screen an object of size 6 cm. The object is at a distance 10 cm from the convergent lens. How far does the screen need to be placed to make the image clean?
Let distance of screen from lens is V magnification
m = v/u
|m| = h1/h0 = |v|/|u|
6/3 = v/10
v = (6 * 10)/3
v = 20 cm
I have been working to figure out this question and am lost. It asks "for what value of x-axle will the two forces provide 1.6 Nm of torque about the axle?"
Hence, 12.484 cm is the length of the axle for which the two forces produce 1.6 Nm of torque.
How can you increase a given lever arm's torque without using additional force?The force should be exerted as closely as feasible to the pivot point, perpendicular to the lever arm.
The torque produced by the two forces about the axle can be computed using the information in the diagram as follows:
Torque = Force x Distance x sin(theta)
Given that the angle is 90 degrees and the force is 10 N, the torque is as follows for the given distance from the axle:
Torque1 = 10 N x (10 cm + Laxle) x sin(90 degrees)
Torque1 = 10 N x (10 cm + Laxle) x 1
Torque1 = 100 N.cm + 10 N.Laxle
With a 30 degree angle and a distance from the axle of 10 cm for the 5 N force, the torque is as follows:
Torque2 = 5 N x 10 cm x sin(30 degrees)
Torque2 = 5 N x 10 cm x 0.5
Torque2 = 25 N.cm
The sum of the torques produced by the two forces represents the overall torque:
Total Torque = Torque1 + Torque2
Total Torque = 100 N.cm + 10 N.Laxle + 25 N.cm
Total Torque = 125 N.cm + 10 N.Laxle
The combined torque produced by the two forces is 1.6 Nm, as stated. In order to find Laxle, we can fix the equation for the total torque to equal 1.6 Nm:
125 N.cm + 10 N.Laxle = 1.6 Nm
125 N.cm + 0.16 N.cm = 10 N.Laxle
124.84 N.cm = 10 N.Laxle
Laxle = 12.484 cm
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The world’s narrowest street, which is located in a small Italian village, is only 43 cm wide. Suppose a fish with a mass of 1.8 kg is hung from a string attached to a stick. The stick, slightly longer than the street is wide, is placed horizontally across the narrow street with each end resting on a windowsill. The fish hangs a horizontal distance of 7.0 cm from the windowsill on the right. If the axis of rotation for the stick is taken to be the end farthest from the fish, what is the magnitude of the torque produced by the fish? Assume the stick has negligible mass.
The magnitude of the torque produced by the fish is approximately 6.34 N·m.
What is Axis of Rotation?In this case, the axis of rotation is at the end of the stick farthest from the fish, and the fish is hanging from a string attached to the stick, so the force is straight down. The distance from the axis of rotation to the fish is the length of the stick minus the distance from the fish to the windowsill on the right:
τ = r × F × sin(θ)
r = 0.43 m - 0.07 m = 0.36 m
The force is the weight of the fish, which we can calculate using the gravitational acceleration near the Earth's surface:
F = m × g = 1.8 kg × 9.81 m/s2 = 17.658 N
The angle between the force and the lever arm is 90 degrees, because the force is straight down and the lever arm is horizontal:
θ = 90 degrees = π/2 radians
Plugging in the values, we get:
τ = r × F × sin(θ) = 0.36 m × 17.658 N × sin(π/2) ≈ 6.34 N·m
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A 57.0-g tennis ball is traveling straight at a player at 21.6 m/s. The player volleys the ball straight back at 24.7 m/s. (a) What is the magnitude of the ball's change of momentum?
P = p2 - p1 = (1.410 k g/s) - (1.234 k g/s) = 0.176 k g/s is the magnitude of ball's momentum shift. The ball's acceleration shift is therefore 0.176 kg/m/s in size.
How does magnitude work?An average man would have given up due of the task's size. earth sciences. The brightness of the a star as seen from Earth is also measured by magnitude.
What unit is magnitude expressed in?Whole numbers & decimal fractions are used to express magnitude. A moderate earthquake of magnitude 5.3, for instance, and a strong earthquake of magnitude 6.3. Since the scale is based on logarithms, an increase in magnitude by a whole number corresponds to a tenfold rise in observed amplitude on a seismogram.
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a river flows south east at 10km/hr and a boat floats upon it with it's bow pointed in the direction of travel . a man walks upon the deck at 2km in a direction to the right and perpendicular to the direction of the boats movement find the velocity of the man with respect to the earth ?
Explanation:
See image below...direction will be SSE
. "No matter where the object is kept, a diverging lens always forms a virtual image" Do you agree? Give reasons.
I'm sorry, but I must correct the statement as it is not entirely true. A diverging lens can form both real and virtual images depending on the position of the object relative to the lens.
If the object is placed between the lens and its focal point, the image formed will be virtual, upright, and reduced in size. This is because the light rays appear to diverge from a point behind the lens, which produces the virtual image. In this case, the image cannot be projected on a screen as the light rays do not actually converge to a point.
However, if the object is placed beyond the focal point of the diverging lens, a real image is formed. The image is inverted and reduced in size, and can be projected on a screen as the light rays converge to a point.
Therefore, it is not entirely true that a diverging lens always forms a virtual image. The position of the object relative to the lens determines whether the image formed is virtual or real.
A highway is to be built between two towns, one of which lies 32.0km south and 72.0km west of the other. What is the shortest length of highway that can be built between the two towns, and at which angle would this highway be directed with respect to due west
The shortest distance that can be travelled by road between the two towns, and at what angle would it face due west is 78.79km and Ф is 23.3°
We can create a right triangle with legs that are 32 km and 72 km apart if we join the tips of the distances from the west and south. The hypotenuse is the unidentified shortest length. The Pythagorean theorem enables us to state that According to the Pythagorean Theorem, The sum of the squares of the lengths of a right triangle's legs equals the square of the hypotenuse's length.
In other words, a² + b² = c² for the triangle depicted below.The right triangle's legs, a and b, are perpendicular sides, and the hypotenuse, c, is the side that faces away from the right angle.
This program is frequently employed in building projects and essentially anything that includes right triangles, like as roofs for homes, and soon.
h² = (32 km)² + (72 km)².
h²=1024+5184
h²=6208
h=√6208
h=78.79km
Angle=tan⁻¹(Ф)
so tan(Ф)=32/72
tan(Ф)=0.444
Ф=tan⁻¹(0.444)
=23.3Degrees
H is equal to 78.79 in terms of value. As a result, the shortest length of the route is about 78.79 km and angleФ is 23.3°.
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