Question

The figure below shows an object with a mass of m = 7.40 kg that starts from rest at point A and slides on a track with negligible friction. Point A is at a height of 5.90 m, point B is at a height of 3.2 m, and point C is at a height of 2.0 m.

(a) What is the object's speed at 3.2 m (in m/s)?

What is the object's speed at 2.0 m (in m/s)?

(b) What is the net work (in J) done by the gravitational force on the object as it moves from point A to point C? J

Answer 1

Applying conservation of energy between point A and B,

7.4xgx5.9 = 1/2x7.4xv2 + 7.4xgx3.2

873.2 = 7.4v2 + 473.6

v = 7.34 m/s

the problem can also be solved by using laws of motion,

to find velocity at C, which has come down to a height of 2 meter, it means it has travelled by 5.9-2 =3.9 m

so, v2 = 2gh = 20x3.9 =

v = 8.83 m/s

Work done by gravity when it moves from A to C = mxgx(5.9-2) = 288.6 joule