A student is asked to measure the acceleration of a glider on a frictionless, inclined plane, using an air track, a stopwatch, and a meterstick. The top of the track is measured to be 1.774 cm higher than the bottom of the track, and the length of the track is d = 127.1 cm. The cart is released from rest at the top of the incline, taken as x = 0, and its position × along the incline is measured as a function of time. For x values of 10.0 cm, 20.0 cm, 35.0 cm, 50.0 cm, 75.0 cm, and 100 cm, the measured times at which these positions are reached (averaged over five runs) are 1.02 s, 1.53 s, 2.01 s, 2.64 s, 3.30 s, and 3.75 s, respectively, (a) Construct a graph of x versus t 2 , with a best-fit straight line to describe the data, (b) Determine the acceleration of the cart from the slope of this graph, (c) Explain how your answer to part (b) compares with the theoretical value you calculate using a = g sin θ as derived in Example 5.6.
A student is asked to measure the acceleration of a glider on a frictionless, inclined plane, using an air track, a stopwatch, and a meterstick. The top of the track is measured to be 1.774 cm higher than the bottom of the track, and the length of the track is d = 127.1 cm. The cart is released from rest at the top of the incline, taken as x = 0, and its position × along the incline is measured as a function of time. For x values of 10.0 cm, 20.0 cm, 35.0 cm, 50.0 cm, 75.0 cm, and 100 cm, the measured times at which these positions are reached (averaged over five runs) are 1.02 s, 1.53 s, 2.01 s, 2.64 s, 3.30 s, and 3.75 s, respectively, (a) Construct a graph of x versus t 2 , with a best-fit straight line to describe the data, (b) Determine the acceleration of the cart from the slope of this graph, (c) Explain how your answer to part (b) compares with the theoretical value you calculate using a = g sin θ as derived in Example 5.6.
Solution Summary: The author explains how the graph of x versus t2 is used to find the acceleration of the cart.
A student is asked to measure the acceleration of a glider on a frictionless, inclined plane, using an air track, a stopwatch, and a meterstick. The top of the track is measured to be 1.774 cm higher than the bottom of the track, and the length of the track is d = 127.1 cm. The cart is released from rest at the top of the incline, taken as x = 0, and its position × along the incline is measured as a function of time. For x values of 10.0 cm, 20.0 cm, 35.0 cm, 50.0 cm, 75.0 cm, and 100 cm, the measured times at which these positions are reached (averaged over five runs) are 1.02 s, 1.53 s, 2.01 s, 2.64 s, 3.30 s, and 3.75 s, respectively, (a) Construct a graph of x versus t2, with a best-fit straight line to describe the data, (b) Determine the acceleration of the cart from the slope of this graph, (c) Explain how your answer to part (b) compares with the theoretical value you calculate using a = g sin θ as derived in Example 5.6.
An
object of mass 5.9 kg moves along a flat surface and then up an incline with a steepness of 7.8°.
If the object is moving with a speed of 12.6 m-s¹ along the flat surface, how fast is it moving (in m-s¹) after it has travelled 2.2 m along the incline?
Assume that the incline is frictionless, and ignore air resistance.
A car is initially at rest on a straight road. The graph shows the speed of the car as a function of time.
v (m/s)
12
11
10
9
8
7
6
5
4
3
2
1
M
Ħ
0 1 2 3 4 5 6 7 8 9 10 11
t(s)
What is the speed of the car at t=7 s?
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How much distance did the car cover in the first 9 seconds?
12 13 14
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Determine the distance covered by the car between t=10 s and t=13 s?
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What is the average speed of the car between t=4 s and t=8 s?
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>V=0
d
(m
A block of mass m is on an inclined ramp. The ramp makes an
angle with respect to the horizontal, as shown. The ramp has
friction, with coefficient of kinetic friction and static friction μs.
This experiment takes place on earth.
The block has an initial speed of v up the ramp. It travels a
distance d along the ramp before it stops.
There are no numbers in this problem! Answer all questions in
terms of the given variables (g, m, µk, µs, 8, v, d) only.
Do not use any other variables.
a) Draw a free body diagram clearly showing all the forces acting on the block while it is moving
up the ramp.
b) Calculate the work done by the Normal force as the block travels the distance d.
Is it positive, negative, or zero?
c) Calculate the work done by the Weight force as the block travels the distance d.
Is it positive, negative, or zero?
d) Calculate the work done by the Friction force as the block travels the distance d.
Is it positive, negative, or zero?
e) If the block comes to rest,…
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