Question

Two lifeguards pull on ropes attached to a raft. If they pull in the same direction, the raft experiences a net external force of 347 N to the right. If they pull in opposite directions, the raft experiences a net external force of 122 N to the left.

Draw a free body diagramfor each situation and find the magnitude of the larger of the two individual forces.

Answer 1

F1 = 234.5

Step-by-step explanation:

F1 = force applied by the first life guard

F2 = force applied by the second life guard

• In the first scenario both lifeguards pull in the same direction and the raft experiences a net force of 347 N

F1 + F2 = 347 ...equation 1

• In the second scenario both lifeguards pull in different directions and the raft experiences a net force of 122 N

F1 - F2 = 122 ....equation 2

• from equation 1 , F1 = 347 - F2 .....equation 3
• substituting equation 3 into equation 2

(347 - F2) - F2 = 122

347 - 2F2 = 122

2F2 =347 - 122

F2 = 225 ÷ 2 = 112.5 N

• substituting the value F2 = 112.5 N into equation 1

F1 + F2 = 347

F1 + 112.5 = 347

F1 = 347 - 112.5 = 234.5 N

Therefore F1 = 234.5 and F2 = 112.5

the larger of the two forces is F1 = 234.5