How Do You Solve AP Physics C Mechanics 2002 Free Response Problem 2?

[cokezero]

Can anyone help me with problem 2 on the 2002 free response section for mechanics:

The cart is mass m and has four solid rubber tires each of mass m/4 and radius r. Each tire has rotational inertia ½ ML2. The cart is released from rest and rolls without slipping from the top of an inclined plane of height h. Express all algebraic answers in terms of the given quantities and fundamental constants.
a. Determine the total rotational inertia of all four tires.
b. Determine the speed of the cart when it reaches the bottom of the incline.
c. After rolling down the incline and across the horizontal surface, the cart collides with a bumper of negligible mass attached to an ideal spring, which has a spring constant k. Determine the distance xm the spring is compressed before the cart and bumper come to rest.
d. Now assume that the bumper has a non negligible mass. After the collision with the bumper, the spring is compressed to a maximum distance of about 90% of the value of xm in part (c). Give a reasonable explanation for this decrease.

a) is just 4 times the inertia
b) is sqrt(10h/2.5)
c) is srt 20mh/k
d) i don't know please help

can anyone verify the rest of my answers

the ? is posted on collegeboard #2 on 2002

 

[berkeman]

It's hard to follow what you are doing. Could you please define a few of the things in your work? Why is -b- what you have written? And in -a-, what "inertia" are you referring to?

 

[cokezero]

sorry about that
so for a i think i have it right since its just asking for the rotational inertia of the 4 spokes. they give the formula for each spoke as ½ ML2; and since the answers are all variables i am assuming its just ½ ML2 + ½ ML2 + ½ ML2 +½ ML2 = total rotational inertia for the spokes

i only really have a ? on parts c and d...how can adding in a mass for the bumper affect the distance the spring compresses?

for b i did gravatational potential energy= Kinetic energy + rotational kinetic energy; mgh=.5mv^2 + IW^2; i then plugged in v/r for w. i then solved for v; v= sqrt 10h/2.5

 

[NTUENG]

Hi cokezero,

I saw your question while doing some questions on rotational motion. For (b),

<< complete solution removed by berkeman >>

For part (c),

<< complete solution removed by berkeman >>


For part (d),

<< complete solution removed by berkeman >>


Hope that helps. Correct me if I'm wrong in anyway.

 

[berkeman]

Hi NTUENG,

Thanks for offering help in the homework forums. But please be careful not to post complete solutions like you did in this thread.

It is against PF homework forum rules to post complete solutions. Our objective is to provide hints and suggestions, and help the student to figure out the problem on their own. Ultimately, we want to help the student learn how to learn the material, not just provide them with the answer.

Thanks again for your help in the homework forums. And welcome to the PF!

 

[NTUENG]

Dear berkeman,

Thanks for the reminder as I'm still new to this forum. I'll follow the forum rules the next time i reply to or post a new message. It's been such a wonderful year for me in my local university in Singapore. Nice to meet u. Where are u from??

Regards
Lin Ruijin

 

[berkeman]

Hi Lin,

I'm in Silicon Valley, in Northern California on the west coast of the United States. I'd prefer to live out in the country (I went through high school out in the rural country in Northern California), but the EE job market is strongest here in Silicon Valley, so I put up with the congestion and traffic.

Thanks again for helping out in the PF.

 

[asdfmosin]

can someone please. give hints as to sovle the problems. thanx

 

[berkeman]

can someone please. give hints as to sovle the problems. thanx

Per the PF homework forum rules, you must show your work in order for us to help you. Please show us what equations you think apply to this class of questions, and then show us how you are starting to apply them. We can go from there.