Getting two Answers : calculating velocity of ball

In summary, Mr. Gale builds a velocity measuring machine, tests it by throwing a ball and box, and finds that the ball travels faster before it hits the box.
  • #1
fishspawned
66
16

Homework Statement



Mr. Gale decides to build his own velocity measuring machine.
His plan is to build a box (mass 2.50 kg) that catches the ball (mass 0.500 kg) being thrown. It then slides across the desk but eventually comes to a stop due to friction (μ = 0.800) between the box and the surface. He thinks that knowing how far the box slides will allow him to calculate the velocity of the ball just before it hits the box. To test this out he throws the ball and the box slides exactly 38 centimeters. Calculate how fast the ball must have been going just before it hit the box.

The Attempt at a Solution



There were two different ways to approach it. But this gave different answers. One of these is wrong.

ATTEMPT 1 : Using Energy
KE of the ball before just before it hits the box = Work done by friction on the box and ball combined

0.5(0.5kg)v^2 = (0.800)(2.50 + 0.5)(9.8)(0.38)
v = 6.0 m/s

ATTEMPT 2 : Using Force and Momentum
friction is net force, calculate velocity, use momentum to calculate initial velocity in ball

f = (2.50 + 0.5)(9.8)(0.800) = 23.52 = ma
therefore a = (23.52)/(2.50 + 0.5) = 7.84 m/s^2
using v^2 = 2ad
v = sqrt((2)(7.84)(.38)) = 2.44 m/s

therefore pi = pf
(0.5)(v) = (2.44)(2.50 + 0.5)
v = 14.64 m/s

why am I getting different values? There is something I am forgetting here.
Thanks for any help in advance
 
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  • #2
Is work conserved in the process of catching the ball?
 
  • #3
i think the assumption i am making is that

KE + Wnc = 0
 
  • #4
fishspawned said:
i think the assumption i am making is that

KE + Wnc = 0
There are two stages here. In the first stage, the ball is caught by the box, in the second the box slides. You have assumed all initial KE is lost in the sliding stage. Is that a safe assumption?
 
  • #5
From what you are saying, I am taking it that the impact of the ball on the box would release some energy before it even begins to slide? Could this be calculated? I assume not without further information. However, now this leads me to even more confusion. Are you suggesting that method 2 is correct?
 
  • #6
fishspawned said:
From what you are saying, I am taking it that the impact of the ball on the box would release some energy before it even begins to slide? Could this be calculated? I assume not without further information. However, now this leads me to even more confusion. Are you suggesting that method 2 is correct?
Method 2 is correct. You can use it to find how much energy was lost in the impact.
Note that for no energy to be lost in the collision it would have to be completely elastic. Newton's "experimental" law tells you that the relative velocity would be negated. That is, the ball and box would move apart just after the collision as fast they approached each other just before the collision.
 
  • #7
Fantastic. The different velocities is giving me a way to calculate the actual energy loss from the impact. That's awesome. This turned out better than i thought. Many thanks for the help.
 

1. How do you calculate the velocity of a ball?

The velocity of a ball can be calculated by dividing the change in position (displacement) by the change in time. This is known as the average velocity formula.

2. What is the formula for calculating velocity?

The formula for velocity is v = Δx / Δt, where v is velocity, Δx is the change in position, and Δt is the change in time.

3. How do you determine the change in position and time for a ball?

The change in position (Δx) can be determined by subtracting the initial position from the final position. The change in time (Δt) can be determined by subtracting the initial time from the final time.

4. Can you calculate the velocity of a ball without knowing the change in time?

No, the change in time is a necessary component in calculating velocity. Without knowing the change in time, it is not possible to accurately determine the velocity of a ball.

5. Does the mass of a ball affect its velocity?

Yes, the mass of a ball does affect its velocity. A heavier ball will require more force to move and will therefore have a slower velocity compared to a lighter ball with the same amount of force applied.

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