Ball-Wall collision problem

  • #1
Problem goes: A rubber ball, travelling in a horizontal direction, strikes a vertical wall. It rebounds at right angles to the wall. The graph below illustrates the variation of the ball’s momentum p with time t when the ball is in contact with the wall.
upload_2018-7-24_14-58-39.jpeg


Which of the following statements is true?

A) The shaded area is equal to the force exerted by the wall on the ball.
B) The shaded area is equal to the force exerted by the ball on the wall.
C) The gradient is equal to the force exerted by the wall on the ball.
D) The gradient is equal to the force exerted by the ball on the wall.

The right answer is C. I understand how the gradient in any momentum vs time graph is the force, but I don’t understand why it’s by the wall on the ball instead of the ball on the wall.
 

Attachments

  • upload_2018-7-24_14-58-39.jpeg
    upload_2018-7-24_14-58-39.jpeg
    32.6 KB · Views: 1,138

Answers and Replies

  • #2
stockzahn
Homework Helper
Gold Member
498
136
Is the ball's momentum positive or negative, when touching the wall at the first time (at ##t=0## in the graph)?
 
  • #3
mjc123
Science Advisor
Homework Helper
1,097
530
The gradient is negative, i.e. away from the wall (the ball's initial momentum is positive, i.e. towards the wall). If it was ball on wall, the gradient would be the same but with opposite sign, i.e. positive. More generally, the force acting on on an object is equal to the rate of change of momentum of the object. So in any graph like that (momentum of an object vs. time), the gradient of the line is the force acting on the object.
 
  • Like
Likes PhysicsIsKillingMe and PeroK
  • #4
Orodruin
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
Gold Member
16,935
6,741
The most straightforward reasoning is to go to Newton's second law, dp/dt = F, where F by definition is the force on the body. Hence, the derivative of the momentum of the ball is equal to the total force acting on the ball, which in this case is provided by the wall.
 

Related Threads on Ball-Wall collision problem

  • Last Post
Replies
24
Views
5K
Replies
2
Views
142
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
12
Views
2K
Replies
3
Views
4K
  • Last Post
Replies
1
Views
8K
  • Last Post
Replies
2
Views
614
Replies
17
Views
3K
Replies
5
Views
679
  • Last Post
Replies
3
Views
7K
Top