How Is Work Done by Friction Calculated on a Quarter Circle Ramp?

[Jtappan]

Homework Statement

Jim rides his skateboard down a ramp that is in the shape of a quarter circle with a radius of 6.50 m. At the bottom of the ramp, Jim is moving at 2.82 m/s. Jim and his skateboard have a mass of 67.0 kg. How much work is done by friction as the skateboard goes down the ramp?
______J

Homework Equations

angular velocity? + frictional force equation?

The Attempt at a Solution

How is the frictional force determined from this without the kinetic friction coefficient?

 

[G01]

In this case you do not actually need the force of friction to find the work done by it.

HINT: Think in terms of conservation of energy. What can this principle tell you about this problem?

 

[ogb p]

I would first gather all the necessary information and equations to solve this problem. The given information includes the shape of the ramp, the radius, the initial velocity, and the mass of Jim and his skateboard. The equations that can be used are the equations for angular velocity and frictional force.

Angular velocity is defined as the rate of change of angular displacement and can be calculated using the formula w = v/r, where w is the angular velocity, v is the linear velocity, and r is the radius. In this case, the angular velocity of Jim's skateboard can be calculated as 2.82 m/s divided by the radius of 6.50 m, which gives us an angular velocity of 0.434 rad/s.

Frictional force, on the other hand, is the force that opposes the motion of an object and can be calculated using the formula Ff = μN, where Ff is the frictional force, μ is the coefficient of kinetic friction, and N is the normal force. Since the coefficient of friction is not given, we can assume that the ramp is made of a material with a low coefficient of friction, such as wood or plastic, and use a value of 0.2 for μ.

Now, to calculate the work done by friction, we can use the formula W = Ff*d, where W is the work, Ff is the frictional force, and d is the distance traveled. In this case, the distance traveled is equal to the circumference of the quarter circle ramp, which can be calculated as 2πr/4 = πr/2. Therefore, the work done by friction can be calculated as:

W = Ff*d = μN*(πr/2) = (0.2)*(67.0 kg)*(9.8 m/s^2)*(π*6.50 m/2) = 663.4 J

In conclusion, the work done by friction as Jim rides his skateboard down the ramp is approximately 663.4 J. However, it is important to note that this is an estimated value since the coefficient of friction was assumed and not given. To get a more accurate value, the actual coefficient of friction for the material of the ramp would need to be known.