A 2-kg box is compressed by an amount of x as shown. The spring constant is 40N/

Question

A 2-kg box is compressed by an amount of x as shown. The spring constant is 40N/m. After being released, the box stops 5-meters away from the equilibrium point. Find X. What is the speed of the box as it passes the equilibrium point? A small cart of 500 grams is moving at 4 m/s on an air track (no friction). It collides with a large-cart of 4 kg at rest. After the collision, the small cart recoils at 1.5 m/s. What is the velocity of the larger cart after the collision? A disk starts from rest, then speeds up with an angular acceleration of 50 md/s. How many revolutions has the disk made?

Explanation / Answer

energy stored in spring = energy lost in friction
0.5*k*x^2 = (mu)mgd
0.5 * 40 * x^2 = 0.2 * 2 * 9.8 * 5
x^2 = 0.98
x = 0.99 m

energy conservation
0.5 * k * x^2 = 0.5 * m * v^2
v^2 = 40*0.99/2
v = 4.45 m/s

momentum conservation
0.5*4 + 0 = 0.5*(-4.5) + 4*v
v = 1.0625

w2^2 = w1^2 + 2a

250^2 = 0 + 2*50*

= 625 rad

no of revolution = 625/2pie = 99.47

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