Solve Momentum Problem: Find Value of 'v

  • Thread starter DeathKnight
  • Start date
  • Tags
    Momentum
In summary, the conversation discusses a problem where a ball is thrown towards a wall with a given speed and rebounds with a different speed, and the coefficient of restitution is 1/3. The question is to find the value of the final speed. The conversation also mentions the use of Newton's law of restitution, and the concept of conservation of momentum in collisions. The solution involves considering the parallel and perpendicular components of velocity and using the given information to find the final speed and angle. The conversation also delves into the idea of momentum transfer and its manifestation in the form of vibrations in the wall.
  • #1
DeathKnight
73
0
Guys I'm having a little problem in undersatnding a few things:
We have a wall and a ball of mass 'm'. The ball is thrown towards the wall with speed u and rebounds with speed 'v'. The coefficient of restitution is, e is 1/3. The question is to find the value of 'v'.
Thats how I think it should be solved:
mu=mv (since the final velocity of the wall is "CONSIDERED" zero)
=> u=v

Now if I apply Newton's law of restitution and simplify:
v=-eu (putting this into u=v gives us)
u=-eu
cancelling u gives e=-1 but e=1/3. Where did I go wrong? I just can't understand it.
Any help will be greatly appreciated.
 
Last edited:
Physics news on Phys.org
  • #2
How can v=u given than e=1/3? The energy need not always be spent in speeding up an object. v = -1/3u.
 
  • #3
Oh my mistake. It is v=-eu. Original post edited.

neutrino said:
How can v=u given than e=1/3?

I asked this question because nowadays we are doing oblique collisions between a wall and a ball in mathematics.
This is an example question(it appeared in exams a few years ago).
Velocity of the ball=u
angle which the ball makes with the smooth wall when it collides=45deg.
angle after collision=theta
velocity after collision=20m/s
e=1/3.
Find u and angle theta.
I've got the answer by considering the component of velocity parallel and perpendicular to the wall. What I want to know is why Law of conservation momentum gives us false result considering it momentum is conserved in ALL collision.
 
  • #4
Lets say you throw the ball against the wall and no energy is lost whatsoever. You would expect the ball to hit the wall and bounce back. If the ball loses no energy, then you also expect that its final speed is equal to its initial speed (in the opposite direction). Now examine it's momentum. Initially it had

p_0 = +mv

while finally it has

P_1 = -mv

This is a net momentum "gain" of |2mv| for the ball in the direction anti-parrallel to its initial velocity. Where has the momentum gone (or come from)?

The answer is that the wall suffers a net "gain" of -|2mv| of momentum. If the wall is fixed then the gain in momentum will be manifest as phonons (vibrations) in the wall. This is why someone else on the other side of the wall would hear you throwing the ball against it.

So momentum is conserved in the entire collision. It's just not very useful for calculating the longitudinal component of momentum for your ball.
 

1. What is momentum and why is it important in science?

Momentum is a measure of an object's motion and is defined as the product of its mass and velocity. It is important in science because it helps us understand and predict how objects will behave when they interact with each other.

2. How do you calculate momentum?

Momentum is calculated by multiplying an object's mass by its velocity. The formula for momentum is p = mv, where p is momentum, m is mass, and v is velocity.

3. What is the unit of measurement for momentum?

The unit of measurement for momentum is kg*m/s (kilogram meter per second) in the SI system. In the imperial system, the unit is lb*ft/s (pound foot per second).

4. How do you solve a momentum problem to find the value of velocity?

To solve a momentum problem and find the value of velocity, you can use the formula p = mv. Plug in the known values for momentum (p) and mass (m), and then solve for velocity (v).

5. Can momentum be negative?

Yes, momentum can be negative. This occurs when an object's velocity is in the opposite direction of its momentum. For example, if an object is moving east and its momentum is defined as positive, if it starts moving west, its momentum will become negative.

Similar threads

  • Introductory Physics Homework Help
Replies
6
Views
821
Replies
1
Views
461
Replies
13
Views
791
  • Introductory Physics Homework Help
Replies
6
Views
728
  • Introductory Physics Homework Help
Replies
2
Views
693
  • Introductory Physics Homework Help
Replies
15
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
793
Back
Top