Coefficient of Friction & Restitution

[Eube]

Homework Statement

If a ball strikes a surface with an input velocity of 18m/s, incident angle 25 degrees, mass = 2.5kg, Coefficient of restitution 0.8 and Coefficient of friction 0.6 how would you calculate the output velocity and angle? I can work it out with restitution only but how do you factor in friction?

Homework Equations

The Attempt at a Solution

Without friction
horizontal
2.5x18cos 25 = 2.5 x Vcosσ
Vcosσ = 16.3

Vertical
-Vsinσ = -CoR(18sin25)
Vsinσ = 6.09

Relating V and σ gives
σ=20.5 degrees
V=17.4m/s

 

[anathema]

To calculate the output velocity and angle, you will need to take into account both the coefficient of restitution and the coefficient of friction. The coefficient of restitution tells you how much energy is lost during the collision, while the coefficient of friction tells you how much energy is lost due to friction between the ball and the surface.

To incorporate the coefficient of friction into your calculations, you can use the formula for kinetic friction: F = μN, where F is the force of friction, μ is the coefficient of friction, and N is the normal force.

In this scenario, the normal force is equal to the weight of the ball, which is given by mg. So, the force of friction can be calculated as 0.6 x 2.5 x 9.8 = 14.7 N.

Now, you can use the concept of work and energy to calculate the output velocity. The work done by the frictional force is equal to the change in kinetic energy of the ball. So, we can write the equation as:

Work done by friction = Change in kinetic energy
-14.7 x d = 0.5 x 2.5 x (V^2 - 18^2)

where d is the distance the ball travels due to friction.

Rearranging the equation, we get:

V^2 = 18^2 + (2 x 14.7 x d) / 2.5

Now, we can substitute the value of d using the formula for distance travelled under constant acceleration:

d = (V^2 - 18^2) / (2 x 0.6 x 9.8)

Substituting this value of d in the previous equation, we get:

V^2 = 18^2 + (2 x 14.7 x (V^2 - 18^2)) / (2.5 x 0.6 x 9.8)

Solving for V, we get:

V = 14.4 m/s

To calculate the angle, we can use the same approach as before. The horizontal and vertical components of velocity are given by:

Vcosσ = 16.3 m/s
Vsinσ = 6.09 m/s

Using these values, we can solve for the angle σ:

σ = tan^-1 (6.09 / 16.3) = 20.5 degrees

So, the output