- #1

- 4

- 0

My AP Physics C class has a test tomorrow about Rotation Dynamics and my teacher gave us a practive exam over the weekend and i felt really good about it thinking i was going to do really well, but this practice exam is really difficult and im stuck on every problem. there are four problems but ill try to get help with them 1 at a time.

A large sphere rolls without slipping(pure rolling) across a horizontal surface. The sphere has a constant translational velocity of 10 m/s, a mass of 25kg, and a radius of 0.2 m. The sphere approaches the 25 degree incline of height 3 m as shown in the attached file and rolls up the incline without slipping. (entire problem and questions attached)

Vo = 10 m/s

m = 25 kg

r = 0.2 m

ϑ = 25 degrees

h = 3 m

(also i'm using g = 10 m/s^2)

KE = 1/2 mv^2 + 1/2 Iw^2

I = 2/5 MR^2 (solid sphere)

TEa = TEb

ok i did parts a and b but im stuck at c, and i feel really stupid for not being able to figure it out but heres what i have so far.

a.) to find the total kinetic energy, i used

KE = 1/2 mv^2 + 1/2 Iw^2 and plugged in the inertia and omega, and solved it down to

KE = 1750 joules

b.) to find the velocity, i used

TEa = TEb for TEa i plugged in 1750 and for TEb i plugged in the kinetich and potential energy.

1750 = 1/2 mv^2 + 1/2 Iw^2 + mgh plugged in everything and solved it down to

v = 7.56 m/s

now part c asks for how far in the x direction it travels after flying off the plane. i know that it will leave the inclined plane in a case 1 trajectory but i have forgotten a lot of the trajectory motion stuff we did at the begining of the year and i have completely forgotten how to find the time. once i have the time i would plug it into Sx=Vo(sin ϑ)t. i have an equation for the time of a case 1 trajectory but the sphere falls another 3 meters after it is level with the point it left from.

if anyone could help me find the time for this spot i would much appreciate it.

-EDIT-

ok i figured out #1 by myself. to find the time you set Sy = -3 and use the equation

Sy = Vo(Sin ϑ)t - 1/2gt^2 plug in and move it around to get the quadratic

0 = -5t^2 = 3.18t - 3 use the quadractic equation and use the positive result as the time

t = 1.16 s

then plug that into

Sx = Vo(Cos ϑ)t plug in all variables and solve

Sx = 7.98 m

I also solved my problems with #2 so i wont post that. but i have some issues on #3 and 4 as well so ill post them next.

## Homework Statement

A large sphere rolls without slipping(pure rolling) across a horizontal surface. The sphere has a constant translational velocity of 10 m/s, a mass of 25kg, and a radius of 0.2 m. The sphere approaches the 25 degree incline of height 3 m as shown in the attached file and rolls up the incline without slipping. (entire problem and questions attached)

Vo = 10 m/s

m = 25 kg

r = 0.2 m

ϑ = 25 degrees

h = 3 m

(also i'm using g = 10 m/s^2)

## Homework Equations

KE = 1/2 mv^2 + 1/2 Iw^2

I = 2/5 MR^2 (solid sphere)

TEa = TEb

## The Attempt at a Solution

ok i did parts a and b but im stuck at c, and i feel really stupid for not being able to figure it out but heres what i have so far.

a.) to find the total kinetic energy, i used

KE = 1/2 mv^2 + 1/2 Iw^2 and plugged in the inertia and omega, and solved it down to

KE = 1750 joules

b.) to find the velocity, i used

TEa = TEb for TEa i plugged in 1750 and for TEb i plugged in the kinetich and potential energy.

1750 = 1/2 mv^2 + 1/2 Iw^2 + mgh plugged in everything and solved it down to

v = 7.56 m/s

now part c asks for how far in the x direction it travels after flying off the plane. i know that it will leave the inclined plane in a case 1 trajectory but i have forgotten a lot of the trajectory motion stuff we did at the begining of the year and i have completely forgotten how to find the time. once i have the time i would plug it into Sx=Vo(sin ϑ)t. i have an equation for the time of a case 1 trajectory but the sphere falls another 3 meters after it is level with the point it left from.

if anyone could help me find the time for this spot i would much appreciate it.

-EDIT-

ok i figured out #1 by myself. to find the time you set Sy = -3 and use the equation

Sy = Vo(Sin ϑ)t - 1/2gt^2 plug in and move it around to get the quadratic

0 = -5t^2 = 3.18t - 3 use the quadractic equation and use the positive result as the time

t = 1.16 s

then plug that into

Sx = Vo(Cos ϑ)t plug in all variables and solve

Sx = 7.98 m

I also solved my problems with #2 so i wont post that. but i have some issues on #3 and 4 as well so ill post them next.

#### Attachments

Last edited: