An empty metal box with a mass of 0.275 kilogram is moved along a conveyor belt at a constant speed of 1.34 m/s before sliding across a frictionless track. The box then slides along a 26.5 centimeter long skid pad (labeled, "Rough Patch", above) designed to slow the box down. After the skid pad, the box moves onto another frictionless track. Shortly after the skid pad, the box is filled with 12.8 kilogram of marbles, which fall from a chute with an initial velocity of 7.67 m/s. Finally, at the end of the production line the box is stopped by a bumper so a factory worker can seal it for shipping.
a. Find the momentum and kinetic energy of the box when it leaves the conveyor belt?
b. If the coefficient of friction of the skid pad is 0.307, determine what is the velocity of the box after crossing the skid pad? (Remember that velocity has a direction!)
c. If the marble chute is at an angle 15.0 degree from the vertical, determine what is the velocity of the full box along the production line after the marbles fall?
d. Sometimes, when the box hits the bumper at the end of the production line, a marble flies off and lands on the floor. If the marble falls from a height of 0.750 meter above the ground, determine what will its velocity be just before it hits the ground?