Question

2. Students are conducting a physics experiment where two equal-mass carts are free to roll on a frictionless surface. As shown above, Cart A starts at rest a height h above the horizontal surface, where Cart B is initially sitting at rest. Cart A rolls down the incline and hits Cart B. The carts stick together after the collision, and the students determine it takes the carts a time of t = 4.0 seconds to travel between two photogates which are placed a distance s = 1.2 meters apart.

(a) Determine the speed that the carts have as they travel together after the collision.

(b) Determine the speed that Cart A had the instant before colliding with Cart B.

(c) Determine the initial height h that Cart A was placed on the inclined surface.

(d) Calculate the decrease in kinetic energy of the two cart system that occurs during the collision.

Answer 1

a)

$$v=\frac{s}{t}=\frac{1.2}{4}=0.3\frac{m}{s}$$

b)

$$mV=(m+m)v\\V=2v=0.6\frac{m}{s}$$

c)

$$h=\frac{V^2}{2g}\\h=\frac{0.6^2}{2(9.8)}=0.018\ m$$

d)

$$\Delta K=0.5(mV^2-2mv^2)\\\Delta K=0.5(4mv^2-2mv^2))=mv^2$$