A 185 g cart is given a push up a frictionless incline, giving it an initial vel

Question

A 185 g cart is given a push up a frictionless incline, giving it an initial velocity of 1.45 m/s. The incline is at an angle of 10.0o to the horizontal. You must show your work to get full credit for this problem.

a) How far up the incline does the cart move before it stops, i.e. the distance along the incline?

b) How much vertical displacement has occurred during its movement up the incline?

c) What is the cart’s initial kinetic energy, i.e. when it leaves the launcher?

d) What is the cart’s change in kinetic energy from the launch point to the point at which it stops?

e) How much work has been done on the cart by gravity as it moved up the incline?

f) Using conservation of energy determine the vertical displacement of the cart, assuming the initial velocity of 1.45 m/s.

Explanation / Answer

v^2-u^2 = 2*a*s

Here v = 0, a = -g*sin(10)

s = u^2/2*g*sin(10) = 0.618m

b) h = s*sin(10) = 0.107 m

c) KEi = 0.5*m*u^2 = 0.1945 J

d) KEf - KEi = -0.1945 J

e) Workdone by gravity = -0.1945 J

f)

0.5*m*v^2 = m*g*h

h = 0.5*v^2/g = 0.107 m

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