Question 40

[Guest]

Dr. Ferdinand,

In the solutions, they add 60 with 200. I am having difficulty in picturing this. I see the centripetal force as pulling inward and tension pointing up (in same direction) the weight (200 N) in the downward direction.

2T + C.F. = Weight and solve for T?

[admin]

First, let's try to really imagine the situation then we'll look at the physics.

If what you are saying is true:

2T + C.F. = Weight

then

2T = Weight - C.F.

then you are saying that as the child swings to the lowest point, the tension in the ropes decreases. That does not seem logical since it is precisely at this point that the tension is greatest (sometimes in physics, it is helpful to imagine the opposite extreme example to clarify a point: clearly at 180 degrees from the bottom, the tension would be very low or nothing).

Now comes some theory about centripetal forces. The problem centers on the following: when you are in an elevator, and accelerate upwards, you feel a little tug downwards as you accelerate.

When you are in a car or an amusement park ride and you turn, you have a component of acceleration which is centripetal (directed towards the center) and you feel the tug in the opposite direction (your body moves away from the center of the circle).

You experience the acceleration in the opposite or centrifugal direction. If you were in the elevator, accelerating upwards while standing on a scale, you would see your "weight" (really your force normal N) increase (mg + ma). Likewise, at the bottom of the swing, the child's "weight" (mg + CF) must also increase.

I hope that helps.

[xueweiz3194]

I still don't understand how centripetal force can point away from the center and in the direction where the weight force is pointing (unless it is not centripetal force we are talking about that is acting in the same direction as the weight force). I thought centripetal force always points toward the center of the circular path.

Is the force that's pointing in the same direction as the weight force centripetal force? If it is, how could it be not pointing to the center? If it isn't, then what force it is?

[nedaa.asba6809]

xueweiz3194;

The force you are referring to is indeed the centripital force. You are correct, the force does point towards the center however because of the inertial properties of mass, the mass will try to maintain its straight line motion and as a result will feel like he's being "forced to the outside". This is a direct result of the centriptal force and you should always maintain as such.

[admin]

Bump.

[GraemeMatt8033]

Centripetal force is not pointing away from center, it is pointing towards center.

Okay so in uniform circular motion, centripetal force keeps it in orbit, the force being directed toward the center. What is providing the centripetal force? Force of Gravity.

So now we have a pendulum. So now that gravity is pointing away from the center, the centripetal force is being provided by the string. So what is making up the force of gravity is:
T=mg +Fc

So the tension in the string is providing the centripetal force, and making up for the remaining force of gravity not compensated by Fc.

Hope that makes more sense

[harrington5609]

So that's why centripetal force always requires another force along with it? Such as tension, gravitation force, magnetic force etc? Makes sense

[RichardParker]

How were we supposed to know that the swing was rotating in the vertical plane and not horizontal plane ?

[mcat_premed3832]

By definition:

1. To move back and forth suspended or as if suspended from above.

www.thefreedictionary.com/swing


I'm not sure if you were thinking of an amusement park ride which is attached by ropes/seats and that turn in circles: for example, www.italintl.com/detail_page.php?record_id=1227

BUT, the speed that it must generate to be truly horizontal would be astronomical (in the true NASA sense! ) .