Solving a Physics Problem with a Bowling Ball

[runningirl]

Homework Statement

Students are playing with the 4.13 kg bowling ball hung from the ceiling of the classroom. When at rest, it hangs 0.63 m above the floor. The cord is 1.87 long. The students pull the ball up and to the side and then let go. It swings back and forth like a pendulum. The students pull it so it is 1.40 m above the ground.

a) What is the ball's velocity when it's at the lowest point? Assume no air resistance.

b) What's the tension in the string at this point?

Homework Equations

The Attempt at a Solution

a) (1/2)mv^2=mgh
.5(4.13)v^2=4.13*9.8*.63
v=3.51 m/s?
b) mgh=F(1.4-.63)
9.8*4.13*.63=F(.77)
F=33.11 N?

I don't know if I did a right, and I don't know how to do b...

 

[Doc Al]

a) (1/2)mv^2=mgh
.5(4.13)v^2=4.13*9.8*.63
v=3.51 m/s?

That's the correct formula, but h represents the change in height. From the highest point to the lowest point, what is the change in height of the ball?

For b you need to use Newton's 2nd law and some facts about circular motion.

 

[runningirl]

um... exactly what would i need for b?
"facts about circular motion" i mean.

Thanks for the help with part a!

 

[runningirl]

um... exactly what would i need for b?
"facts about circular motion" i mean.

Thanks for the help with part a!

 

[runningirl]

Oh. I get it now.

a=v^2/r
F=ma
Just find F.

Thanks!

 

[Doc Al]

a=v^2/r
F=ma
Just find F.

Almost. F is the net force. There are two forces acting on the ball. One is the tension, which is what you need to find.

 

[runningirl]

Fnet=mg+tension?
but mg=-9.8(4.13)
so i could easily find tension?

 

[cepheid]

Fnet=mg+tension?
but mg=-9.8(4.13)
so i could easily find tension?

Yes, that's exactly the idea. You can find the tension because you know mg, and you know F_net (what must it be equal to?).