Solve Collision Velocity: Mass, Friction & Impulse

In summary, the conversation discusses the calculation of the speed of a ball and the initial velocity of a block in a collision scenario. The ball's speed is determined to be 5.4 m/s using the formula mgh=mv^2/2. The block's initial velocity is calculated to be 1.0368 m/s using the formula 2.592/2.5, but this is found to be incorrect due to not accounting for the friction that causes the block to come to rest. The conversation concludes that the impulse of the ball and the block must be equal and that the change in momentum of the ball (5.4^2 * 0.48/2) is not equivalent to the change in momentum
  • #1
Drizzy
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Homework Statement



A ball with the mass 0.48kg is hanging on a string. The ball is moved to the side and then released . When the string is vertical, the ball hits the side of a block which is at rest . The ball's position is then 1.5 lower down than from the beginning.

a) the speed gets the ball ?

I used the formulas mgh=mv^2/2 and the answer is 5.4 m/s

b) The block has a mass of 2.5 kg. The block slides 0.65 m on the floor before stopping. The friction coefficient is 0.20. What is the block's initial velocity when hit by the ball?

2. Homework Equations
3. The Attempt at a Solution

Now this is where it gets tricky. The ball's impulse must be the same as the impulse of the block. The ball's impulse is 0.48 * 5.4 = 2.592 . So that menas that the block's ivelocity 2,592 / 2.5 = 1,0368 m/s But it is wrong and I do not understand why.

One of Newtons law says that the impulse is the same in a collision.
 
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  • #2
Drizzy said:
The block has a mass of 2.5 kg. The block slides 0.65 m on the floor before stopping. The friction coefficient is 0.20. What is the block's initial velocity when hit by the ball?
Forget about the ball. You have all the information needed to analyze the block.

Drizzy said:
Now this is where it gets tricky. The ball's impulse must be the same as the impulse of the block. The ball's impulse is 0.48 * 5.4 = 2.592 . So that menas that the block's ivelocity 2,592 / 2.5 = 1,0368 m/s But it is wrong and I do not understand why.
You assume the ball stops dead. Don't.
 
  • #3
oh so the impulse is the same only if one of the objet stops?

hmm I have seen some people say that the work of the friction is equal to the ball's energy but I don't understand why
 
  • #4
Drizzy said:
oh so the impulse is the same only if one of the objet stops?
No, but you do not have enough information to calculate the impulse. At least not yet.

Drizzy said:
hmm I have seen some people say that the work of the friction is equal to the ball's energy but I don't understand why
It is friction that makes the block come to rest.
 
  • #5
oh i forgot... thanks so much !
 
  • #6
i think i have enough information because the imoulse is the change in momentum. So the change in momentum of the ball is 5,4^2 * 0,48/2
 
  • #7
Drizzy said:
i think i have enough information because the imoulse is the change in momentum.
Do not assume you know the final speed of the ball after the collision.

Drizzy said:
So the change in momentum of the ball is 5,4^2 * 0,48/2
That's the kinetic energy of the ball just before the collision.
 
  • #8
okay now i know why thank you
 

1. How do you calculate collision velocity?

To calculate collision velocity, you will need to use the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. The value of a can be calculated using the formula a = ∑F/m, where ∑F is the sum of all the forces acting on the object and m is the mass of the object.

2. How does mass affect collision velocity?

Mass is directly proportional to collision velocity. This means that the higher the mass of an object, the higher its collision velocity will be. This is because an object with a higher mass has a greater inertia and requires more force to accelerate, resulting in a higher collision velocity.

3. What role does friction play in collision velocity?

Friction is a force that opposes motion and acts in the opposite direction of an object's velocity. In a collision, friction can reduce the object's velocity and absorb some of the kinetic energy. This means that the higher the friction, the lower the collision velocity will be.

4. How is impulse related to collision velocity?

Impulse is the change in momentum of an object and is directly related to collision velocity. The greater the impulse, the greater the change in velocity, resulting in a higher collision velocity. Impulse can be calculated using the formula J = FΔt, where J is the impulse, F is the force, and Δt is the time interval.

5. How can collision velocity be reduced?

Collision velocity can be reduced by increasing the time of impact, decreasing the mass of the object, or increasing the force of friction. This can be achieved by using safety equipment, such as airbags, or by designing structures with materials that can absorb and dissipate energy during a collision.

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