Dynamics Example 1 © 2000 D.P. Maloney

A boat that is traveling in a straight line at 6 m/s picks up speed so that 12 sec. later it is traveling at 27 m/s. If the mass of the boat plus occupants is 1600 kg, what was the net force on the boat?

Physical (Mathematical) Principles and/or Ideas: kinematic relations for constant

acceleration motion, and basic relation (Newton’s second law) for force.

Solution: Let’s consider what is happening in the problem to see if that can provide us with some guidelines about how to proceed. We have a boat that increases its speed in a certain time. That means it is accelerating. Since we know the boat’s initial and final speeds and the time it took to change the speed, we can use the basic kinematic relation for acceleration. (Since nothing was said about the boat changing direction, we assume it is moving in a straight line). Once we know the acceleration, we can multiply it by the mass to obtain the net force. So let’s carry out this program. The basic kinematic relation for acceleration is:

Next, we multiply this by the mass of the boat to find the net force. This is Newton’s second law.

Questions: How does this net force we have just calculated relate to the forces shown in the free-body diagram?

We have said all forces are interactions requiring agents and objects. Does this apply to the net force also? If no, why not? If yes, what are the agent and object?