A small cart of mass starts from rest at the top of a smooth track above ground level
PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power
Problem
A small cart of mass 1.5kg starts from rest at the top of a smooth track 4m above ground level. The track first descends to ground level and then rises smoothly up another hill. Neglect air resistance unless stated otherwise. Take g=9.8m s−2.
(i) Derive an expression for the speed v of the cart when it is at a height h above the ground (0≤h≤4m).
(ii) Calculate the speed of the cart at the lowest point of the track.
(iii) Assuming the second hill is frictionless, determine the maximum height above the ground that the cart can reach before momentarily coming to rest.
(iv) If, while climbing the second hill, the cart loses 3J of mechanical energy due to friction, find the new maximum height it can attain.