Question

A 45-kg child sits on a 3.2-kg tire swing. What is the tension in the rope that hangs from a tree branch?

Answer 1

@wolfe8

Answer 2

So tension would be the net force acting on a connection against it's normal condition(i.e a rope is held in place at the branch but the weights pulls it down). Here the connection is the rope, and the weights it is supporting are the child and the tire with both exerting force downwards because of gravity. So the net(total) force acting onto the rope is? And here you are given the mass in kg. Keep in mind that tension is a force, and force is? Hint: second law of motion)

Answer 3

Net(total) would be 45+3.2?

Answer 4

Yes, but that is the total mass. I should have said that earlier instead of asking for total force. So now how do you convert mass to weight/force, again?

Answer 5

Is it the same w=mg formula?

Answer 6

Yes. But to be exact, force F = ma. But since here the acceleration is toward earth because of gravity, a=g. So use earth's gravitational pull.

Answer 7

So F=48.2(9.8)

Answer 8

Yes

Answer 9

There's a second part to the question. The tree branch sags and the child's feet rest on the ground. If the tension in the rope is reduced to 222N, what is the value of the normal force being exerted on the child's feet?

Answer 10

See normal is the force acted by a surface onto another surface that comes in contact with it. So if the child is standing on the ground, the normal is exerted by the ground onto the child's feet and the swing system since they are one. So you have the weight of the child and swing acting downward, and the normal acting upward. You are given the net force. What do you do?

Answer 11

So subtract 220 from the answer in the other problem and multiply by 9.8?

Answer 12

Wait. Subtract 220 from the answer and then divide by 9.8?

Answer 13

Nevermind. I'm confused...

Answer 14

Well you already have both in the same unit(meaning same category: force). So here: Net tension = tension of child and swing - normal = 222

We do this because net is the total, yet normal is acting in the opposite direction as the weight. So we subtract instead.

Answer 15

@wolfe8 Sorry I had to go somewhere, can you explain this to me?