How can I calculate the initial velocities for a ball rolling off a ramp?

Question

In my lab, I have to calculate the initial velocities of different trials for a ball rolling off a ramp. I had thought that the initial velocity would be zero but my teacher said that that's not it. So I decided to use t=0 and plug it into
x=x0+v0*t+(1/2)*a*t^2 but that gives me an intial velocity of zero too. So yeah, i need help.
Oh yeah, my range for the first trial, the distance the ball traveled, was 75cm.

I'm not exactly sure how the ball was rolled off the ramp since I didn't do it but I think it was placed at the beginning of the ramp and naturally rolled down. The only things that I know are:
1. the height of the top of the ramp from the floor (varies)
2. the length of the ramp (100cm); the distance continues on the floor.

Answer 1

it would be v0

the formula x=x0+v0xt+0.5xaxt^2, plugging in t=0 gives you x=x0 distance, so I'm not quite sure where you get initiail velocity=0

there should be a formula where

v=v0+axt, (this is derived from x=x0+v0xt+0.5xaxt^2)

so at t=0, v=v0

Answer 2

It appears you are missing some information. The ball is apparently given some initial velocity which you are supposed to figure out. the only measurement you have is the height and length of the ramp, and the distance the ball rolls from the end of the ramp. What is needed here is the coefficient of friction of the ball, and if it is the same both on the ramp and on the floor. If you know this coefficient you can find the initial velocity. The energy of the ball at the top of the ramp is m*g*h + .5*m*v0^2; h is the height of the ramp, m = mass of the ball. The energy used by falling down the ramp and rolling is Fr(floor)*d+Fr(ramp)*L (d = roll distance on the floor, L = ramp length. Fr(floor) = µf*m*g, Fr(ramp) = µr*m*g*cos(T), where µf and µr are the coefficients of friction of the floor and ramp, and T is the angle the ramp makes with the floor, which is arcsin(h/L). Do the energy balance:

.5*m*v0^2+m*g*h = Fr(ramp)*L + Fr(floor)*d

.5*m*v0^2+m*g*h = µr*m*g*cos(T) + µf*m*g

and solve for v0.

(You will note that every term involves m, so it cancels out and you don't need to know it.)

Answer 3

If you are starting the ball from rest then the initial velocity is 0. If it is not starting from rest then the initial velocity is v0 in your equation.

Answer 4

A.) Calculate the rotational inertia of the ball Use right here to remedy: a million/2v^2 x ( mass + (inertia/radius^2)) = mgh B.) Calculate the rotational kinetic skill of the ball. Use right here to remedy: rotational KE = a million/2 x inertia x omega(rad/s)^2 omega = angular velocity in rad/s = 5m/s / radius = one hundred rad/s

Answer 5

1:the velocity could be =sin(angle of the ramp)*g(gravitational acceleration)
2:need more details...