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.
A space shuttle lands on a distant planet where the gravitational acceleration is 2.0 ( We do not know thelocal units of length and time , but they are consistent throughout the problem). The shuttle coasts along aleve, frictionless plane with a speed of 6.0. It then coasts up a frictionless ramp of height 5.0 and angle 0f 30°.After a brief ballistic flight, it lands a distance S from the ramp. Solve for S in local units of length. Assume theshuttle is small compared to the local length unit and that all atmospheric effects are negligible. Use x and y components.
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 1.80x10^4 kg semi-trailer truck drives up a 200 m hill [θ = 30 degrees above horizontal], at a constant speed of 25.0 m/s. The force of friction is 6.00x10^2 N. Write an equation to isolate and solve for P.
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