Calculating Deceleration and Force in Circular Motion

[dphin]

2 questions, that I just can't get and anyone's help would be greatly appreciated...

A belt runs on a wheel of radius 44cm. During the time the wheel takes to coast uniformly to rest from an initial speed of 1.8 rev/s, 29.5m of belt length passes over the wheel. Find:
(a) the deceleration of the wheel
(b) the number of revolutions it turns while stopping

A 6.2g arrow moving at 23.2 m/s strikes a watermelon and drills a 75cm hole straight through it. It takes the arrow 0.0375s to emerge from the watermelon. What is the average force that opposes the arrow's motion?

Thanks again for any help you can provide.

 

[NateTG]

Show us what you've tried doing.

It's also probably better to post one problem at a time.

 

[dphin]

Regarding the belt question...

I started with theta=r/s, so .44m/29.5m and got 0.015 rev.

To answer a. I used the final velocity squared= initial velocity squared + (2) (alpha)(theta) and got an answer of:
(1.8 rev/s)squared + (2)(alpha)(0.015 rev)
= 108 rev/s squared.

for b. wouldn't it just be 0.015 revolutions?

 

[dphin]

Any further help would be great?? Thanks a lot.

 

[NateTG]

The wheel should make more than 20 revolutions.

Don't you think you should be using the circumference of the wheel somewhere?

Why are you dividing the diameter of the wheel by the length of belt?

 

[dphin]

I'm sorry, but I'm soooo confused! The circumference is 0.25 m, but then what?? I don't get it.

 

[Doc Al]

Originally posted by dphin
I'm sorry, but I'm soooo confused! The circumference is 0.25 m, but then what?? I don't get it.

So... the circumference is less that the radius? How did you calculate it?

 

[Doc Al]

Originally posted by dphin
Regarding the belt question...

I started with theta=r/s, so .44m/29.5m and got 0.015 rev.

To answer a. I used the final velocity squared= initial velocity squared + (2) (alpha)(theta) and got an answer of:
(1.8 rev/s)squared + (2)(alpha)(0.015 rev)

Several problems here. As NateTG discussed, you messed up the calculation of the number of revolutions. Also, recheck your use of that equation. Ask yourself: What's the final velocity? What's the sign of the acceleration?

 

[dphin]

Sorry about that, dumb mistake I didn't square the radius. Circumerence equals 1.22m (C=(2)(pie)(R^2). The accelerations is negative, therefore decreasing. Is it wrong to use theta=s/r? ...

 

[Doc Al]

You can measure "theta" (angular "distance") in revolutions or in radians, but don't mix them up. Be consistent.

Rewrite your kinematics equation with the correct final angular velocity, angular acceleration, and angular distance.

 

[dphin]

Thank you ...so far you're my favorite! Your clues lead me in a direction I can follow!