Question

A cart is attached to a hanging mass by a string that passes over a pulley. a) Draw free-body diagrams for the cart and the hanging mass (Clearly label all forces present and indicate their relative magnitudes) when the cart is moving:(i) on a horizontal track.(ii) up a track inclined at an angle .b) When the cart moves on an incline at constant speed, it is in equilibrium; i.e., the net force on it is zero. Does it require more, less, or the same tension in the string to pull the cart up the track at constant speed or down the track at constant speed? Explain your answer.c)Derive an equation for the work done by friction when the cart is moving up the track at constant speed. Show your work.

Answer 1

a)

b)

while moving Up , force equation is given as

T - f - mg Sin = 0

T = f + mg Sin              eq-1

while moving down , force equation is given as

mg Sin - T - f = 0

T = mg Sin - f             eq-2

so from these equations Tension T is less while moving down

c)

Work done by friction is given as

W = f d Cos180 = - fd

frictional force is given as

f = _k F_n

But F_n = m_c g Cos

so f = _km_c g Cos

Work done by friction is given as

W = - _km_c gd Cos