1) A cart is traveling at a constant velocity at 30 m/s. If 20 kg of rocks were
ID: 2214313 • Letter: 1
Question
1) A cart is traveling at a constant velocity at 30 m/s. If 20 kg of rocks were put into the cart while it was traveling and the final velocity after all the rocks are put in is 14 m/s, what is the mass of the cart?
2) If I push a mass of 25 kg at a constant velocity of 5 m/s over a surface with coefficient of friction 0.3, what is the force with which I am pushing?
3) Assume I drop a ball at a height of 10 meters and it bounces back to a height of 8 meters.
a. How much energy is lost during the collision?
b. Assuming the collision with the ground lasted 0.1 seconds, what was the average force that the ground exerted on the ball?
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Explanation / Answer
1.) Energy of cart + stone should be conserved
1/2* m* 30^2( Kinetic energy of cart) + 1/2 * 20 * 0 (KE of stone) = 1/2*(m+20)*14^2
450m= 98m + 1960
m=5.568 kg
2.) since velocity is constant the force of push = force of friction
force of friction = *R
R= mg= 25 * 9.8=245
so force = 245 * 0.3 = 73.5 N
3.)( a) Energy lost = Initial Potential energy - final potential energy
potential energy = mgh
energy lost= mg*10 - mg*8= 2mg= 2*m*9.8= 19.6m ( where m is the mass of the ball.)
(b) velocity of the ball just after the strike can be found by equalling potential energy to kinetic energy
mgh= 1/2mv^2
m*9.8*8=1/2 *m*v^2
v=12.52
energy = force *displacement= force*velocity*time
8mg= F * 12.52*0.1
F=62.62m ( m being the mass of the ball)
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