Two people pull as hard as they can on ropes attached to a 170 kg boat. If they pull in the same direction, the boat has an acceleration of 1.59 m/s2 to the right. If they pull in opposite directions, the boat has an acceleration of 0.518 m/s2 to the left. What is the force exerted by each person on the boat? (Disregard any other forces on the boat.)
To find the force exerted by each person on the boat, we can use Newton's second law of motion which states that F = ma, where F is the force, m is the mass, and a is the acceleration.
Let's define the force exerted by the first person as F1 and the force exerted by the second person as F2.
When they pull in the same direction, the boat has an acceleration of 1.59 m/s^2 to the right. So the equation becomes:
F1 + F2 = m * a
Substituting the values:
F1 + F2 = 170 kg * 1.59 m/s^2
Now, when they pull in opposite directions, the boat has an acceleration of 0.518 m/s^2 to the left. So the equation becomes:
F1 - F2 = m * a
Substituting the values:
F1 - F2 = 170 kg * 0.518 m/s^2
So we have a system of equations:
F1 + F2 = 270.3 N
F1 - F2 = 88.06 N
To solve these equations, we can add the two equations together:
(F1 + F2) + (F1 - F2) = 270.3 N + 88.06 N
2F1 = 358.36 N
Divide both sides by 2 :
F1 = 179.18 N
Now we can substitute this value back into one of the equations to solve for F2:
179.18 N + F2 = 270.3 N
Subtract 179.18 N from both sides:
F2 = 270.3 N - 179.18 N
F2 = 91.12 N
Therefore, the force exerted by the first person (F1) is 179.18 N, and the force exerted by the second person (F2) is 91.12 N.