In the figure below, a small block of mass m = 0.019 kg can slide along the fric
ID: 1778742 • Letter: I
Question
In the figure below, a small block of mass m = 0.019 kg can slide along the frictionless loop-the-loop, with loop radius R = 11 cm. The block is released from rest at point P, at height h = 6.8R above the bottom of the loop.
(a) How much work does the gravitational force do on the block as the block travels from point P to point Q? (in Joules)
(b) How much work does the gravitational force do on the block as the block travels from point P to the top of the loop? (in Joules)
If the gravitational potential energy of the block–Earth system is taken to be zero at the bottom of the loop, find the following.
(c) the potential energy when the block is at point P (in Joules)
(d) the potential energy when the block is at point Q (in Joules)
(e) the potential energy when the block is at the top of the loop (in Joules)
(f) If, instead of being released, the block is given some initial speed downward along the track, do the answers to (a) through (e) increase, decrease, or remain the same?
Explanation / Answer
a) mass of block = 0.019kg
R = 11cm=0.11m
h=6.8R=6.8*0.11=0.748 m
as blcok moves from P to Q, work done by gravity = 0.019*9.8*(0.748-0.11)=0.1188 Joule
b)Work done by gravity when block moves from P to top of loop = 0.019*9.8*(0.748-0.22)=0.0983 Joule
c)potential energy of block at P = 0.019*9.8*0.748=0.1393 Joule
d)potential energy of block at Q = 0.019*9.8*0.11=0.0205 Joule
e)the answers to parts (a) through (d) will remain same even if the block is released with some initial velocity.