An object with mass 3.3 kg is executing simple harmonic motion, attached to a spring with spring constant 260 N/m . When the object is 0.017 m from its equilibrium position, it is moving with a speed of 0.40 m/s . Part A Calculate the amplitude of the motion. Express your answer to two significant figures and include the appropriate units.
Answer: the amplitude of the motion is 0.048 m
Explanation:
Given that;
mass m = 3.3 kg
spring constant k = 260 N/m
When the object is x = 0.017 m from its equilibrium position,
it is moving with a speed of v = 0.40 m/s
amplitude of the motion = ?
we know that;
formula for Potential of the string PE = 1/2kx²------1
Kinetic energy KE = 1/2mv² --------2
Now expression for the maximum potential energy of the spring is
PE_max = 1/2 kx²_max -----3
Now from conservation of Energy
PE_spring = PE + KE
from our equation 1, 2 and 3
1/2kx²_max = 1/2kx² + 1/2mv²
now we rearrange for x_max
x²_max = (1/2kx² + 1/2mv²) / 1/2k
x²_max = (kx² + mv²) / k
x_max = √ [(kx² + mv²) / k]
now we substitute our values into the equation
x_max = √ [(260(0.017)² + 3.3×(0.40)²) / 260]
= √((0.07514 + 0.528) / 260)
= √(0.60314 / 260)
= √ 0.002319
x_max = 0.048 m
Therefore the amplitude of the motion is 0.048 m
A swimmer speeds up from 1.1 m/s to 3.2 m/s during the last 13.0 seconds of the race. What is the acceleration of the swimmer?
Answer:
a = 0.16 [m/s²]
Explanation:
To solve this problem we must use the following equation of kinematics.
[tex]v_{f}=v_{o}+a*t\\[/tex]
where:
Vf = final velocity = 3.2 [m/s]
Vo = initial velocity = 1.1 [m/s]
t = time = 13 [s]
a = acceleration [m/s²]
Now replacing:
[tex]3.2=1.1+a*13\\2.1=13*a\\a=0.16[m/s^{2} ][/tex]
Total internal reflection at the air liquid surface is observed for an unknown liquid when the angle of incidence is 43 degrees. What is the index of refraction of this unknown liquid?
a. 0.68
b. 1.0
c. 1.47
d. 1.59
Answer:
c. 1.47
Explanation:
Snell's law states that there exists always a fixed relationship between the index of refraction of two transparent media, and the sines of the incident and refraction angles, as follows:[tex]\frac{n_{i} }{n_{r} } = \frac{sin_{\theta r} }{sin_{\theta i} } (1)[/tex]
When there is a total internal reflection, this means that light can't go across the border between two media, i.e., the refraction angle is 90º, which means that sin θr = 1Since the refraction index for air is 1, i.e. nr =1, this means that (1) , for total internal reflection becomes:[tex]n_{i} = \frac{1}{sin_{\theta i} } = \frac{1}{sin 43} = 1.47 (2)[/tex]
Energy Transformation
A car with a mass of 2000 kg is traveling down the highway at a constant 20 m/s. How much kinetic energy does it have?
100 J
50 J
400.000 J
40.000 J
Answer:
K =400000 J
Explanation:
Kinetic Energy
Is the energy an object has due to its state of motion. It's proportional to the square of the speed.
The equation for the kinetic energy is:
[tex]\displaystyle K=\frac{1}{2}mv^2[/tex]
Where:
m = mass of the object
v = speed at which the object moves
The kinetic energy is expressed in Joules (J)
The car has a mass of m=2000 Kg and travels at v=20 m/s. Calculating the kinetic energy:
[tex]\displaystyle K=\frac{1}{2}2000*20^2[/tex]
Calculating:
K =400000 J
A 125 g pendulum bob hung on a string of length 35 cm has the same period as when the bob is hung from a spring and caused to oscillate. What is the spring’s elastic constant?a) 3.5 N/mb) 5.2 N/mc) 1.9 N/md) 27 N/m
Answer:
k = 3.5 N/m
Explanation:
It is given that the time period the bob in pendulum is the same as its time period in spring mass system:
[tex]Time\ Period\ of\ Pendulum = Time\ Period\ of\ Spring-Mass\ System\\2\pi \sqrt{\frac{l}{g}} = 2\pi \sqrt{\frac{m}{k}[/tex]
[tex]\frac{l}{g} = \frac{m}{k}\\\\ k = g\frac{m}{l}[/tex]
where,
k = spring constant = ?
g = acceleration due to gravity = 9.81 m/s²
m = mass of bob = 125 g = 0.125 kg
l = length of pendulum = 35 cm = 0.35 m
Therefore,
[tex]k = (9.81\ m/s^2)(\frac{0.125\ kg}{0.35\ m})\\\\[/tex]
k = 3.5 N/m
weight of Ali is 500andN.he is standing on the ground with an area of 0.025 m^2 area .we can find pressure under his feet. what is it?
Answer:
20000 Pa
Explanation:
Pressure is defined as the force per unit area.
Mathematically : P =F/A where F is force and A is area
Force = 500 N
Area= 0.025 m²
P= 500/0.025
P= 20000 Pa
1. If an object does not change its position, then we say that it is at _________?
2. According to the video, can an object ALWAYS seem at rest to everyone?
3. What else did the person need in the video to find their friend's house BESIDES a REFERENCE POINT?
4. So according to the video, in order to find an object or place, you need what 3 things?
5. Using the number system to determine motion, what was the starting position of the car in the problem?
6. What was the final position of the car?
7. How far in total did the car actually travel?
Answer:
ᏌᎳᏆᎿᏌᎭ ᎭᏆᎳ ᎷᎭᏌ Ꭽ
Explanation:
Answer:
rest
Explanation:
if an object is not in it's position, then we say it is at rest.
Exercising helps reduce?
Answer:
stress,depression and anxiety by improving self esteem.
A baseball accelerates at 15m/s2, changing its velocity from 0m/s to 50 m/s down the way. How long did it take the baseball to accelerate?
Answer:
3.33s
Explanation:
Given parameters:
Acceleration = 15m/s²
Initial velocity = 0m/s
Final velocity = 50m/s
Unknown:
Time taken for the acceleration = ?
Solution:
To solve this problem, we must understand that acceleration is the rate of change of velocity with time.
Mathematically;
a = [tex]\frac{v - u}{t}[/tex]
a is the acceleration
v is the final velocity
u is the initial velocity
t is the time taken
So;
15 = [tex]\frac{50 - 0}{t}[/tex]
15t = 50
t = 3.33s
A 10-mm-diameter cable is strung between a series of poles that are 50 m apart. Determine the horizontal force this cable puts on each pole if the wind velocity is 34 m/s.
Answer:
The value is [tex]F = 562.7 \ N[/tex]
Explanation:
From the question we are told that
The diameter is [tex]d = 10 \ mm = 0.01 \ m[/tex]
The distance between the poles is L = 50 m
The velocity of the wind is [tex]v = 34 \ m/s[/tex]
Generally the horizontal force the cable puts on each other is mathematically represented as
[tex]F = \frac{1}{2} * C_D * \rho * v^2 * A[/tex]
Here A is the area of the rope(i.e assuming the rope to be a cylinder ) which is mathematically represented as
[tex]A = L * d[/tex]
=> [tex]A = 0.01 * 50[/tex]
=> [tex]A = 0.5[/tex]
Here [tex]C_D[/tex] is the coefficient of discharge of the rope and the value is [tex]C_D = 1.5[/tex]
[tex]\rho[/tex] is the density of air with value [tex]\rho = 1.225 \ kg/m^3[/tex]
So
[tex]F = \frac{1}{2} * C_D * \rho * v^2 * A[/tex]
=> [tex]F = \frac{1}{2} * 1.5 * 1.225 * 34^2 * 0.5[/tex]
=> [tex]F = 562.7 \ N[/tex]
The batter swings and misses the 40 m/s (90 mph) fastball, and the ball (mass 150 grams) ends up at rest in the catcher's mitt. How much work does the catcher perform on the ball
Answer:
The work done by the catcher is 120 J.
Explanation:
Given;
velocity of the fastball, v = 40 m/s
mass of the fastball, m = 150 g = 0.15 kg
Based on work-energy theorem, the work done by the catcher is equal to the kinetic energy of the fastball.
The kinetic energy of the fastball is given as;
K.E = ¹/₂mv²
K.E = ¹/₂ x 0.15 x 40²
K.E = 120 J
Therefore, the work done by the catcher is 120 J.
Mary and John are seated on a bench a distance 2 part. Suddenly, John moves closer to Mary and claims that he has been drawn by the gravitational force. Is John’s claim justifiable? Show quantitatively. (Assume the masses of John and Mary are 67 and 55 respectively, and the coefficient of static friction between John and the bench is 0.15). [4]
Answer:
no
gravitational force between them is far smaller than the frictional force between the guy and the bench
Forces that cancel each other are called_ forces \
Answer:
balanced forces
Two forces of 50 N and 30N respectively, are acting on an object. Find the net force (in N) on the object if
A) the forces are acting in the same direction.. B) Together, forces are acting in opposite directions
Answer:
A) 80 N
B) 20 N
Explanation:
A) If the forces acting are in the same direction, then the net force will be a sum of both so many faces..
Thus;
ΣF = 50 + 30
ΣF = 80 N
B) If the forces are acting in the in opposite directions with the larger force pointing in the positive y-axis then, the net force is;
ΣF = 50 - 30
ΣF = 20 N
A car with an initial speed of 6.50 m/s accelerates at a uniform rate of 0.920 m/s2 for
3.60 s. Find the final velocity.
Answer:
v = 9.812 m/s
Explanation:
Given that,
The initia speed of a car, u = 6.5 m/s
Acceleration of the car, a = 0.92 m/s²
Time, t = 3.6 s
We need to find the final velocity of the car. Let the final velocity be v. Using equation of motion to find it as follows :
v = u +at
Putting all the values,
v = 6.5+(0.92)(3.6)
v = 9.812 m/s
So, the final velocity of the car is 9.812 m/s.
The amount of inertia of an object depends on its __________________________________.
The greater the ________________________________, the greater its _______________________________.
The greater the _____________________________ of the object, the greater the ___________________________
required to accelerate or slow down the object.
The greater the ____________________________ applied, the greater the acceleration.
Answer:
first one :
the object will stay at the same speed and direction unless it is acted upon by an internal unbalanced force.
Please help meeeee
For a velocity versus time graph how do you know what the velocity is at a certain time? How do you know the acceleration at a certain time?
Answer:
Explained below
Explanation:
For a velocity time graph, the y - axis will represent velocity while the x - axis will represent time.
Now, to calculate velocity at a certain time t, we will draw a perpendicular line from the time on the x-axis to the graph line and trace the horizontal line from that point to the y-axis which will give the corresponding velocity at that time.
Now, for the acceleration at a time t. After getting the velocity like explained above, we now divide the velocity by the time.
define electric potential at a point and find expression for it.
Answer:
Recall that the electric potential is defined as the potential energy per unit charge, i.e. V=PEq V = PE q . ... The equation for the electric potential due to a point charge is V=kQr V = kQ r , where k is a constant equal to 9.0×109 N⋅m2/C2.
Explanation:
PLEASE HELP ME!! I NEED ANSWERS ASAP!!!!
Answer:
I do not know the answer because not all of the information is there.
Explanation:
Answer:
Beep Beep
Explanation:
motion is a change in
How does light move?
Answer:
Light travels as a wave. But unlike sound waves or water waves, it does not need any matter or material to carry its energy along. This means that light can travel through a vacuum—a completely airless space. It speeds through the vacuum of space at 186,400 miles (300,000 km) per second.
Explanation:
Hope this helps :))
A contact lens is made of plastic with an index of refraction of 1.60. The lens has an outer radius of curvature of 2.08 cm and an inner radius of curvature of 2.48 cm. What is the focal length of the lens?
Answer:
The value [tex]f = 21.49 \ cm[/tex]
Explanation:
From the question we are told that
The index of refraction is [tex]n = 1.60[/tex]
The outer radius of curvature is [tex]R = 2.08 \ cm = 0.0208 \ m[/tex]
The inner radius is [tex]r = 2.48 \ cm = 0.0248 \ m[/tex]
Generally from Maker's equation we have that
[tex]\frac{1}{f} = [n - 1 ][\frac{1}{(R)} - \frac{1}{r} ][/tex]
=> [tex]\frac{1}{f} = [1.60 - 1 ][\frac{1}{( 0.0208 )} - \frac{1}{0.0248} ][/tex]
=> [tex]\frac{1}{f} = 4.65[/tex]
=> [tex]f = 0.2149 \ m[/tex]
=> [tex]f = 21.49 \ cm[/tex]
if an atom has two protons and three electrons than the atom is
Answer:
negative 1 charge
Explanation:
one electron is extra so there will be -1 chargw
If an atom has two protons and three electrons than the atom is negatively charged.
What is an atom?An atom is a matter particle that defines a chemical element uniquely. An atom is made up of a central nucleus and one or more negatively charged electrons.
The nucleus is positively charged and contains one or more protons and neutrons, which are relatively heavy particles.
It is made up of protons, which have a positive charge, and neutrons, which do not have any charge. Protons, neutrons, and the electrons that surround them are long-lived particles found in all natural atoms.
The modern atomic hypothesis was founded by John Dalton, a great chemist. His atom, on the other hand, was like a solid billiard ball.
An atom is negatively charged if it has two protons and three electrons.
Thus, the given atom bears negative charge.
For more details regarding atoms, visit:
https://brainly.com/question/1566330
#SPJ2
A rock from a volcanic eruption is launched straight up into the air with no appreciable resistance Which one of the following statements about this rock while it is in the air is correct
what kind of law of motion A car still moves for a short period even after the brakes
have been applied.
Answer:
inertia of motionExplanation:
.... ...
you pick up a 3.8 kg can of paint from the ground a lift it to a height of 1.4 m. you hold the can stationary for half a minute, waiting for a friend on a ladder to take it. how much work do you do duting this time (when the can of paint is stationary)?
Answer:
No work
Explanation:
During the time of holding the can stationary, no work is being done by the person carrying the can.
The can is simply at rest.
Work is done when a force is applied to move a body through a certain distance.Work done = force x distance
In the instance given in this problem, only when the paint was lifted up is work done.
When the paint is stationary and being supported by the person, no work is done.
Comparing infrared and ultraviolet, we can say that __________. Comparing infrared and ultraviolet, we can say that __________.
Answer:
The appropriate response will be "Infrared has a longer wavelength and lower photon energy".
Explanation:
This same Infrared emission falls between some of the observable but rather microwave components of the electric spectrum. Infrared rays have quite a wavelength longer than ultraviolet light. And indeed the frequency of radiation remains smaller, unlike UV rays. Even before we recognize that the energy (photon) of the visible region has always been equal to the total of waves. Infrared thus has smaller photon intensity versus ultraviolet.when does a circuit is said to be over loaded?
Answer:
Every electric circuit in a wiring system must be protected against overloads. A circuit overload occurs when the amount of current flowing through the circuit exceeds the rating of the protective devices. The amount of current flowing in a circuit is determined by the load -- or the "demand" -- for current.
Explanation:
Hope this helps :)
A 1.0 kg object is attached to a 0.50 m string. It is twirled in a horizontal circle above the ground at a speed of 5.0 m/s.
The direction of the acceleration at the point shown points towards which letter?
Given that,
Mass of the object, m = 1 kg
It moves in a circle of radius 0.5 m with a speed of 5 m/s
To find,
The direction of the acceleration.
Solution,
Whenever an object moves in a circular path, the only force that acts on its is centripetal force which is given by the formula as follows :
[tex]F=\dfrac{mv^2}{r}[/tex]
The centripetal acceleration acts in the direction of force. It acts along the radius of the circular path. In this figure, the direction of the acceleration is shown at point d.
Answer:
D!
Explanation:
took the test
Plz help
Fill in the blank with the correct observation from the simulation.
As the days go on, the distance that the moon is from the sun in the night sky
A. Stays the same
B. Decreases
C. Increases
Starting at New Moon, The visual distance increases for about 2 weeks, then decreases for about the next 2weeks, until the next New Moon.
On the average, it changes by about 12° per day.