Two lifeguards pull on ropes attached to a
raft. If they pull in the same direction, the raft
experiences a net external force of 376 N to
the right. If they pull in opposite directions,
the raft experiences a net external force of
162 N to the left.
Draw a free body diagram for each situation
and find the magnitude of the larger of the two
individual forces.
Answer in units of N
Eq1: F1 + F2 = 376 N.
Eq2: F1 - F2 = 162 N.
Sum: 2F1 = 538
F1 = 269 N.
In Eq1, replace F1 with 269:
269 + F2 = 376
F2 = 376 - 269 = 107 N.
In the first scenario where the lifeguards pull in the same direction and the raft experiences a net external force of 376 N to the right:
Free body diagram:
- Raft: The raft will have a force applied to the right (376 N) due to the lifeguards pulling in that direction.
In the second scenario where the lifeguards pull in opposite directions and the raft experiences a net external force of 162 N to the left:
Free body diagram:
- Raft: The raft will have a force applied to the left (162 N) due to the lifeguards pulling in opposite directions.
To find the magnitude of the larger of the two individual forces, we can compare the magnitudes of the forces applied to the raft in each scenario.
In the first scenario, the force applied to the right is 376 N.
In the second scenario, the force applied to the left is 162 N.
Since 376 N is greater than 162 N, the larger of the two individual forces is 376 N.
To solve this problem, we first need to draw two free body diagrams: one for when the lifeguards pull in the same direction, and one for when they pull in opposite directions.
1. Same direction:
In this case, both lifeguards are exerting a force to the right, so the net external force on the raft is 376 N to the right. To represent this on the free body diagram:
- Draw an arrow pointing to the right to represent the net external force of 376 N.
- Label this arrow as the net external force.
2. Opposite directions:
In this case, one lifeguard is exerting a force to the right, while the other is exerting a force to the left. The net external force on the raft is 162 N to the left. To represent this on the free body diagram:
- Draw an arrow pointing to the right to represent the force exerted by the lifeguard pulling to the right.
- Draw an arrow pointing to the left to represent the force exerted by the lifeguard pulling to the left.
- Label the arrow pointing to the right as force 1.
- Label the arrow pointing to the left as force 2.
- Draw an arrow pointing to the left to represent the net external force of 162 N.
- Label this arrow as the net external force.
Now, to find the magnitude of the larger of the two individual forces, we can use the fact that the net external force is the vector sum of the individual forces.
When the lifeguards pull in the same direction, the net external force is 376 N to the right. This means that the individual forces must also add up to 376 N in the same direction. Since both forces are in the same direction, the magnitude of the larger individual force is 376 N.
When the lifeguards pull in opposite directions, the net external force is 162 N to the left. This means that the individual forces must add up to 162 N in opposite directions. Since one of the forces is pulling to the right and the other to the left, we can subtract the two forces to find the magnitude of the larger force. So, the magnitude of the larger individual force is 376 N - 162 N = 214 N.
Therefore, the magnitude of the larger of the two individual forces is 214 N.