Question

A small boat coasts at constant speed under a bridge. A heavy sack of sand is dropped from the bridge onto the boat. The speed of the boat

a. does not change.
b. increases.
c. Without knowing the mass of the boat and the sand, we can't tell.
d. decreases

Answer 1

The speed of the boat decreases when a heavy sack of sand is dropped onto it while it coasts at constant speed. This outcome is due to the conservation of momentum in the system, where the increase in mass leads to a decrease in speed to conserve the initial momentum.

Step-by-step explanation:

When a heavy sack of sand is dropped onto a small boat that coasts at constant speed under a bridge, the initial impact will be an external force acting on the system of the sand and the boat. According to Newton's third law of motion, the sack of sand will exert a force on the boat when it hits, but we should consider the conservation of momentum to understand the speed of the boat after the sand lands in it. If we assume the system is closed and there are no external forces after the impact, the total momentum of the system must be conserved.

Before the sack is dropped, the momentum of the system is just the momentum of the boat since the sack is at rest with respect to the bridge. When the sack lands on the boat, their combined mass increases. Since momentum must be conserved (the product of mass and velocity before and after the event must be equal), the speed of the boat decreases to compensate for the greater mass of the combined system. Therefore, the correct answer is (d) decreases.

Answer 2

d. decreases

Step-by-step explanation:

The law of conservation of momentum tells us that the sum of momenta before the collision is equal to the sum of momenta after the collision. The bag has no momentum as it falls onto the boat because its velocity is zero in the horizontal direction. But after it hits the boat, it's momentum increases while the momentum of the system remains the same. That means a component of the system must decrease somewhere else. And that component is the velocity, not the mass, of the boat.