Inclined plane (A ball rolling down a slope)

[inb4physics]

Homework Statement

The mass of the ball: 136 G
Length of the slope that its sliding down: 132 Cm
Angle of the slope that its sliding down: 11,5228 °

All I have to do, is to find the velocity, and the acceleration of the ball. Though my teacher has given us no time at all for this project, and due to many projects overlapping my 3 current physics projects, which are still in progress of being made. I would be grateful if you guys could provide me with the formulas. I can find the moment of inertia, and the impuls force myself.

The Attempt at a Solution

a=g*sin(v)-(u)*cos(v)

v^2=2*V[m/s^]*D => v=V[m/s]

 

[barryj]

You might start by finding the velocity at the bottom of the ramp.
PE is convertd into KE.

 

[inb4physics]

so mgh = 1/2mv^2, and then isolate V?

 

[barryj]

Consider the angular KE also

 

[inb4physics]

So after isolating the equation, then add *cos^-1(ω) ?

 

[barryj]

Think of it this way.
mgh = (1/2)mv^2 + (1/2)I omega^2

 

[inb4physics]

mgh = (1/2)mv^2 + (1/2)I omega^2

Could you explain the last part of that equation? Omega, what does that stand for?

 

[barryj]

kinetic energy (rotational) = (1/2) (moment of inertia) (angular velocity)^2
Note: the problem didn't state whether this is a solid ball or a shell, like a basketball. This is important in knowing the moment of inertia

 

[inb4physics]

Its a sort of marble. Its made out of hard rock materials.

 

[barryj]

There are actually two ways you can approach this problem. One is the way I have proposed, and another is to draw a freebody diagram of the ball and figure out all the forces and torques. Remember, once you have the velocity at the bottom and the distance covered, you can figure out the average acceleration.

 

[inb4physics]

How can I know the angular velocity, if I don't know the velocity nor the Acceleration?

 

[barryj]

Recall that tyhe angular velocity is related to the linear velocity..

(omega) = velocity X radius

 

[haruspex]

How can I know the angular velocity, if I don't know the velocity nor the Acceleration?

In dealing with the energy, the acceleration doesn't matter. You don't need to know either velocity individually, you just need to know the relationship between them. That means you can write your energy equation with only one unknown.

 

[barryj]

Let me explain without giving you the answer.
If the ramp was frictionless, then the ball would slide and not rotate. However if there is friction and the ball doesn't slide, then it will start to rotate. So, if there is rotation, then you must consider the linear kinetic energy at the bottom of the ramp as well as the rotational kinetic energy. The linear KE is (1/2)mv^2 the rotational KE is (1/2)Iw^2. w is the angular or rotational velocity and I the moment of inertia. The reason I asked about whether the ball was solid or a shell is because they have different moments of inertia. You can determine w from the radius of the ball and the linear velocity of the ball. When you put all of this together properly, you can solve for v at the bottom of the ramp.

 

[inb4physics]

One thing that I still wonder is, how that I can find the angular velocity? Doesn't that require that I know the velocity at first? (Sorry that I ask this much)

 

[Doc Al]

One thing that I still wonder is, how that I can find the angular velocity? Doesn't that require that I know the velocity at first? (Sorry that I ask this much)

Since the ball rolls without slipping, the angular and linear velocities are connected. (As barryj already stated.) You can express one in terms of the other and solve for both.

 

[inb4physics]

So the angular velocity just turns into regular velocity? I am just still curios as to what the angular velocity might be, just can't imagine it.

 

[Doc Al]

So the angular velocity just turns into regular velocity?

No, but they are related. If you know one, you know the other. (Or you would if you knew the radius.)

 

[barryj]

I don't want to give you the answer but... remember that the angular velocity is the linear velocity divided by the radius of the ball.