A student conducts oscullation experiments with a low friction cart on a horizon
ID: 1344885 • Letter: A
Question
A student conducts oscullation experiments with a low friction cart on a horizontal track. The cart is connected to one end of the track by a spring. (The spring is fastened to the left side of the cart, so that a cart motion to the left tends to compres the spring.) The cart is pulled 10 cm to the right from the equilibrium position and released from rest. It is observed to move back and forth with simple harmonic motion.
1. At the instant the cart is at its farthest postion to the left, is the acceleration to the left, to the right, or zero? Explain
2. State hour each of the following single changes would affect the magnitude of the cart's acceleration at the instant it is at its farthest position to the left.
i. The cart is pulled 20 cm to the right and released from reast. Explain
ii. An extra mass is fastened to the cart (but the cart is still pulled 10 cm and released). Explain
iii. A second spring, identical to the first, is added in parallel to the original spring. (The new spring provides a second, identical connection between the cart and the end of the track.). Explain
Explanation / Answer
From Newton’s 2nd law F=ma, the maximum acceleration will occur wherever the net force is a maximum.
For a spring, F = - K*s, so the maximum force occurs at the maximum value for s (displacement from equilibrium).
(1)
At the instant the cart is at its farthest postion to the left. acceleration will be Maximum towards right.
(2)
(i)
As we know, F = - K*s,
If we Increases s, Force would increase and so would Acceleartion.
Acceleartion would Increase.
(ii)
We Know, F = m*a
If we Increases mass , But Force remains the same , Therefore Acceleartion would Decrease.
Acceleartion would Decrease.
(iii)
In This Case there would be no Change in Acceleration.
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