A 700 g cart is released from rest 2.00 m from the bottom of a frictionless, 30-
ID: 1493374 • Letter: A
Question
A 700 g cart is released from rest 2.00 m from the bottom of a frictionless, 30-degree ramp. The cart rolls down the ramp and bounces off a rubber block at the bottom. The collision lasts 25 ms and the cart experiences an average collision force of 175N during the collision. Use concepts of energy, impulse, and momentum to answer following questions.
First make a sketch and indicate the coordinate system you are going to use Show your calculations and indicate which principles you are using.
What is the speed of the cart just before it hits rubber block?
What is the magnitude of the impulse on the cart?
What is the magnitude of the impulse on the rubber block?
What is the speed of the block just after it bounces off the rubber block?
How much energy is lost during the collision?
Is the momentum of the cart conserved in this collision?
Explanation / Answer
All calculations are done in Lab co-ordinates and the orinciples of momentum and energy conservation are used.
mass of the cart m= 700g
inclination 30 deg.
height on ramp = 2m
actual height from ground h = 2Sin(30) = 1m
PE = 0.7*9.8*1 J
KE = PE when the cart reached the bottom
What is the speed of the cart just before it hits rubber block?
speed at the bottom of the ramp v = sqrt(2gh) = sqrt(2*9.8*1) = 4.43 m/s
What is the magnitude of the impulse on the cart?
impulse = 175*25e-3 = 4.375 N-s
What is the magnitude of the impulse on the rubber block?
It is same as on the cart = 4.375 N-s
What is the speed of the block just after it bounces off the rubber block?
change in momentum of the cart = 0.7*4.43 - 4.375 = -1.3175
speed of the cart after impact = -1.3175/0.7 = -1.875 m/s
-ve sign indicates the cart is moving in oppsite direction
How much energy is lost during the collision?
energy last = 0.7(4.432 - 1.8752)/2 = 5.64 J
Is the momentum of the cart conserved in this collision?
Momentum is not conserved as some momentum is aborbed by the rubber block which is at rest. It is an inelastic collision.
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