# Physics

posted by .

A solid ball and a hollow ball, each with a mass of 2 kg and radius of 0.1 m, start from rest and roll down a ramp of length 2 m at an incline of 34°. An ice cube of the same mass slides without friction down the same ramp.

What is the speed of the solid ball at the bottom of the incline?

The answer is 3.96 m/s. How do I get this answer? At first I thought I could use E=1/2mv^2; however, I do not have the total amount of energy, so I cannot use this equation. Any help is greatly appreciated.

• Physics -

For each object
PE → KE
h =s•sinα = 2•sin34º =1.12 m

Solid ball I = 2•m•R²/5, ω=v/R
PE =KE = KE (translational) + KE (rotational)
m•g•h = m•v²/2 + I•ω²/2 = m•v²/2 + 2•m•R²•v²/2•5R² =
= m•v²/2 + m• v²/ 5 =0.7•m• v².
v = sqrt(g•h/0.7) =sqrt(9.8•1.12/0.7) =3.96 m/s.

Hollow ball I = 2•m•R²/3 , ω=v/R
m•g•h = m•v²/2 + I•ω²/2 = m•v²/2 + 2•m•R²•v²/2•3R² =
= m•v²/2 + m• v²/ 3 =5•m• v²/6.

Ice cube
m•g•h = m•v²/2

## Similar Questions

1. ### Physics

A ball rolls down an incline at a constant acceleration of 2 m/s^2. What is the velocity of the ball after 8.5 s?
2. ### Physics HELP!!!

A ball (radius 0.2 m) is rolling on level ground toward an incline. If its velocity is 3 m/s, to what maximum height above the ground does it roll up the incline?
3. ### Physics

1. A hollow sphere and a solid sphere roll without slipping down two different ramps. They start at different heights. The speed and kinetic energy of each sphere is the same when they reach the bottom of their ramp. If the hollow …
4. ### physics

A solid ball and a hollow ball, each with a mass of 6 kg and radius of 0.1 m, start from rest and roll down a ramp of length 3 m at an incline of 31°. An ice cube of the same mass slides without friction down the same ramp. What is …
5. ### physics

"A solid cylinder and a thin-walled hollow cylinder have the same mass and radius. They are rolling horizontally along the ground toward the bottom of an incline. They center of mass of each cylinder has the same translational speed. …
6. ### physics

"A solid cylinder and a thin-walled hollow cylinder have the same mass and radius. They are rolling horizontally along the ground toward the bottom of an incline. They center of mass of each cylinder has the same translational speed. …
7. ### Physics

A solid and a hollow ball, each with a mass of 1 kg and radius of 0.1 m, start from rest and roll down a ramp of length 3 m at an incline of 35 degrees. An ice cube of the same mass slides without friction down the same ramp. Which …
8. ### Physics

A solid ball and a hollow ball, each with a mass of 2 kg and radius of 0.1 m, start from rest and roll down a ramp of length 3 m at an incline of 44°. An ice cube of the same mass slides without friction down the same ramp. What is …
9. ### physics

A hollow cylinder, a solid cylinder, a hollow sphere, and a solid sphere roll down a ramp without slipping, starting from rest. The ramp is 0.25 m high. All the objects have radius 0.035. What are their final speeds?
10. ### Physics

A solid ball is released from rest and slides down a ramp that makes an angle of 50 degrees with respect to the horizontal. a) What is the minimum coefficient of static friction between the ramp and the ball for no slipping to occur?

More Similar Questions