Physics
Physics
Problem
A lump of clay of mass slides along a horizontal, frictionless table with a speed of and sticks to an initially stationary cart of mass placed on the same table. (i) Find the speed of the cart–clay system immediately after the collision. (ii) After moving together for a while, the clay drops vertically through a hole in the cart without exerting any horizontal force on the cart during its fall. Determine the horizontal speed of the cart just after the clay has left it. (iii) Calculate (a) the percentage loss of kinetic energy during the collision and (b) the additional percentage loss of the system’s kinetic energy that occurs when the clay separates from the cart.Intuitive explanation
PART (I)
This is a perfectly inelastic collision where momentum is conserved but kinetic energy is not. Since the table is frictionless and there are no external horizontal forces, the total momentum before collision equals the total momentum after—use this to find the combined speed.
PART (II)
Once the clay drops vertically through the hole, it no longer exerts a horizontal force on the cart, so the cart's horizontal momentum is no longer affected. The key insight is that the cart's horizontal velocity remains constant during the clay's fall—there's nothing to change it.
PART (III)
For the collision, compare the kinetic energy before and after using the speeds from parts (i) and (ii). For the separation, recognize that dropping vertically means the clay takes away no horizontal momentum, so the cart keeps its speed from part (ii)—the energy loss comes from the clay losing its horizontal motion while the cart keeps moving.
Intuitive explanation
PART (I)
This is a perfectly inelastic collision where momentum is conserved but kinetic energy is not. Since the table is frictionless and there are no external horizontal forces, the total momentum before collision equals the total momentum after—use this to find the combined speed.
PART (II)
Once the clay drops vertically through the hole, it no longer exerts a horizontal force on the cart, so the cart's horizontal momentum is no longer affected. The key insight is that the cart's horizontal velocity remains constant during the clay's fall—there's nothing to change it.
PART (III)
For the collision, compare the kinetic energy before and after using the speeds from parts (i) and (ii). For the separation, recognize that dropping vertically means the clay takes away no horizontal momentum, so the cart keeps its speed from part (ii)—the energy loss comes from the clay losing its horizontal motion while the cart keeps moving.