Understanding Force and Momentum in Angular Elastic Collisions

[PhysicS FAN]

Homework Statement

In the elastic collision (of the image) the sphere has a mass m=1kg and the angles that the object meets and leaves the wall are 60deegres. The time duration of the impact is Δt=0,01 sec and the velocity at which the sphere is moving is u=10√3 m/s. Assume √3= 1,73.

1. What is the change of the momentum
2. What is the force of the wall

Relevant Equations

ΔΚ= W, P=mu

The speed of the sphere after the impact will be the same since the collision is elastic and the kinetic energy remains the same. So the change of momentum will be given by the cosine law right? What bothers me is the second question about the force that acts on the sphere (which can be given by Δp/Δt=ΣF). I can not understand the behavour of the force at the change of direction of the sphere. What I mean is where should I draw the force?

 

[hutchphd]

What is the direction of the change of momentum??

 

[PhysicS FAN]

What is the direction of the change of momentum??

Well the momentum of the sphere before the collision and the momentum after create a 120 deegres angle and so the change will be the distance of the beginning of the first and the end of the last momentum arrow

 

[hutchphd]

Did the momentum parallel to the wall change?

 

[hutchphd]

so the change will be the distance of the beginning of the first and the end of the last momentum arrow

this is not correct. You wish to subtract the initial vector from the final.

 

[haruspex]

the change will be the distance of the beginning of the first and the end of the last momentum arrow

As @hutchphd writes, that is incorrect; that is how to find the sum of vectors diagrammatically.
To find the change, you can draw both vectors from the origin and find the vector that goes from the end of the first to the end of the second.