Hi everyone, I have a Physics problem that I need a hand with:
Two people pull as hard as they can on ropes attached to a boat of mass 200 kg. If they pull in the same direction, the boat has an acceleration of 4 m/s^2. If they pull in opposite directions, the boat has an acceleration of 2 m/s^2. What is the force exerted by each person on the boat? Disregard any other forces on the boat.
Thank You!!

Question

Hi everyone, I have a Physics problem that I need a hand with:
Two people pull as hard as they can on ropes attached to a boat of mass 200 kg.  If they pull in the same direction, the boat has an acceleration of 4 m/s^2.  If they pull in opposite directions, the boat has an acceleration of 2 m/s^2.  What is the force exerted by each person on the boat?  Disregard any other forces on the boat.
Thank You!!

anonymous · Answer

If we say that the force exerted by each person is $F_1 \text{ and } F_2$, then we can also say The sum of these forces is equal to the total force on the boat ($=200\times4=800N \text{ or } =200 \times 2 = 400N$). When they are pulling in the same direction, we can say that both forces have the same sign:$$F_1+F_2=800$$When they are pulling in opposite directions, we can say that one of the forces is negative: $$F_1-F_2=400$$Which you can solve as simultaneous equations.

anonymous · Answer

Muchos Gracias.  Great answer!