Ii. At the instant shown in Figure 3, the blocks are moving toward each other with the same speed of 0.35m/s. The blocks collide 0.50 seconds later. What is the speed of the two-block system’s center of mass just before the blocks collide?

2.9 m/s

Explanation:

The speed of the two-block system center of mass will not be changed by the collision, since it is an internal force. The only force acting upon the two-block system, then, will be gravity. We can calculate the effects of gravity upon the speed of the blocks along the slope by taking the sine of the angle of the slope (37°) and multiplying it by the magnitude of Fg in the vertical direction. sin(37°)*(3.92 N) = 2.36 N. This force acts upon the system and accelerates it down the slope, which can be modeled with the equation 2.36 N = (0.40 kg)*a. Solving for a, we find that gravity accelerates the block at 5.9 m/s2 along the slope of the block. Using this figure, we can find the speed of the system with the equation v = v0 + at. Initial velocity of the system is zero, as both blocks are moving towards each other at equal speed, so v = (5.9 m/s2)*(0.50 s). Velocity of the system after 0.50 seconds = 2.9 m/s.