Answer:
A. As the ropes are horizontal the child has travelled 2m of vertical displacement from his lowest position.
Gpe @ A=mgh=40*9.81*2=784.8J
B. At 30degree vertical angle the vertical displacement from lowest position is given by
2-2cos(30)=2-1.73=0.27m
Gpe @B= 40*9.81*0.27=106 J
C: at the bottom of circular arc it's Gpe is zero relative to lowest position as bottom of arc itself is lowest position.
(a) The gravitational potential energy when the ropes are horizontal is 784.8 J.
(b) The gravitational potential energy when the ropes make a 30 degree angle with vertical is 106 J.
(c) At the bottom of circular arc the gravitational potential energy is zero.
Given data:
The mass of child is, m = 40.0 kg.
The length of ropes is, L = 2 m.
The energy possessed by any object under the influence of gravity and by the virtue of position of object is known as gravitational potential energy.
(a)
As the ropes are horizontal the child has travelled 2m of vertical displacement from his lowest position. Then the gravitational potential energy is,
[tex]PE = mgL\\\\PE = 40 \times 9.8 \times 2\\\\PE=784.8 \;\rm J[/tex]
Thus, the gravitational potential energy when the ropes are horizontal is 784.8 J.
(b)
At 30 degree vertical angle the vertical displacement from lowest position, the gravitational potential energy is given by,
[tex]PE = mgL(1-cos30^{\circ})\\\\PE = 40 \times 9.8 \times 2 \times (1-cos30^{\circ})\\\\PE = 106 \;\rm J[/tex]
Thus, the gravitational potential energy when the ropes make a 30 degree angle with vertical is 106 J.
(c)
At the bottom of circular arc it's gravitational potential energy is zero relative to lowest position as bottom of arc itself is lowest position.
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