Solving Elastic Collision Homework: Average Force on a 100g Ball

[slanderson113]

Homework Statement

A 100 g ball bounces off a wall elastically. Its initial speed is 3 m/s perpendicular to the wall. If the collision lasts for 10 ms, what is the average force exerted by the wall on the ball?

Homework Equations

F=ma
Conservation of energy & momentum (?)
F=dP/dt

The Attempt at a Solution

I know to find average force the equation is m(vf-vi)/change in time. And in the equation were given the mass, time, and initial velocity, but to finish I need the final velocity but the conservation of energy and momentum, shows it should be the same as the initial making the force zero, however that's not one of the options. Please help!

 

[tiny-tim]

welcome to pf!

hi slanderson113! welcome to pf!

… the conservation of energy and momentum, shows it should be the same as the initial …

no, momentum is a vector, and it'll be opposite

 

[Doc Al]

And in the equation were given the mass, time, and initial velocity, but to finish I need the final velocity but the conservation of energy and momentum, shows it should be the same as the initial making the force zero, however that's not one of the options. Please help!

Realize that velocity is a vector and thus direction matters. The direction of the velocity is represented by its sign. (Do you still think that the initial and final velocities are the same?)

 

[slanderson113]

Oh my gosh thank you guys so much!

 

[rwisz]

I would approach this problem by first considering the principles of conservation of energy and momentum. In an elastic collision, both energy and momentum are conserved. This means that the total kinetic energy and the total momentum of the system before and after the collision must be equal.

In this case, the ball has an initial kinetic energy of 1/2mv^2 and an initial momentum of mv. After bouncing off the wall, its final kinetic energy will also be 1/2mv^2, but its final momentum will be -mv, since it is now traveling in the opposite direction. Therefore, we can set up the following equations:

1/2mv^2 = 1/2mv^2
mv = -mv

Solving for v, we get v=0. This means that the final velocity of the ball after the collision is 0 m/s, and therefore the average force exerted by the wall on the ball is also 0 N.

This may seem counterintuitive, but remember that in an elastic collision, the objects involved do not experience any loss of energy. The wall is able to absorb and then return the ball's kinetic energy without exerting any force on it. Therefore, the average force is 0 N.

In conclusion, based on the principles of conservation of energy and momentum, the average force exerted by the wall on the 100 g ball in this elastic collision is 0 N.