Average force exerted by a wall on a ball

In summary, a 3.72 kg steel ball strikes a wall at 15.1 m/s at an angle of 58.6 degrees with the plane of the wall. It bounces off with the same speed and angle after being in contact for 0.198 seconds. Using the equations for change in momentum and average force, the average force exerted on the ball by the wall is -295.61771 N. However, due to possible differences in significant figures, the exact answer may vary. The change in momentum parallel to the wall is disregarded as it is zero.
  • #1
Agent M27
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0

Homework Statement


A 3.72 kg steel ball strikes a massive wall at 15.1 m/s at an angle of 58.6 with the plane of the wall. It bounces off with the same speed and angle. If the ball is in contact with the wall for .198s what is the average force exerted on the ball by the wall? Answer in units of N.

The picture is depicted with the wall along the y-axis and the ball is originating from the 3rd quadrant with an angle of 58.6 between the trajectory and the negative x axis. It then bounce off and continues into the second quadrant making the 58.6 angle with the negative x-axis again.

Homework Equations



(1) [tex]\Delta[/tex]Px = -mvfcos[tex]\theta[/tex]-mvicos[tex]\theta[/tex]

(2) [tex]\Delta[/tex]Py = mvfsin[tex]\theta[/tex] - mvisin[tex]\theta[/tex]

(3) Favg=[tex]\frac{dP}{dt}[/tex]

The Attempt at a Solution



So I began by using EQ 1 and subbing in known values and arrived at an answer of -58.53231 N s. I then use that value in EQ 3 and arrive at a final answer of -295.61771 N. The online module doesn't give me the correct answer but says this is incorrect. Where am I going wrong? Thanks

I also tried using the angle between the y-axis and the trajectory which gave me an angle of 31.4. This yielded an answer of -95.89 N s. Subbing that into EQ 3 I get an answer of 484.2995 N, yet again this is wrong...

Joe
 
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  • #2
Your numbers seem OK to me. I assume they just want the magnitude of the force. (As to which one is correct, it depends on what that angle is with respect to. "an angle of 58.6 with the plane of the wall" sounds like your second calculation.)

Sometimes those on-line systems can be picky about significant figures. (Some insist on 3 sig figs.)
 
  • #3
Ya this system requires at least 6 sig figs, which is why I gave those long answers. I am going to have to ask my professor because I tried both of those answers with a negative and positive, and still they are registering incorrect. Am I correct in assuming the reason I can disregard change of momentum in the y direction because it is still traveling in the positive why direction, is that a correct assumption? Thanks

Joe
 
  • #4
Agent M27 said:
Am I correct in assuming the reason I can disregard change of momentum in the y direction because it is still traveling in the positive why direction, is that a correct assumption?
Sure. You're not really disregarding it. The change in momentum parallel to the wall is zero.
 
  • #5
I can't believe I spelled the word why when referring to the y axis... I had a chukle at that one. Anyway. Thanks for the description, it makes more sense that way.

Joe
 

Related to Average force exerted by a wall on a ball

1. What is the formula for calculating the average force exerted by a wall on a ball?

The formula for calculating the average force exerted by a wall on a ball is F = m * (v2 - v1)/t, where F is the average force, m is the mass of the ball, v2 is the final velocity of the ball after bouncing off the wall, v1 is the initial velocity of the ball, and t is the time taken for the ball to bounce off the wall.

2. How does the angle of incidence affect the average force exerted by a wall on a ball?

The angle of incidence does not directly affect the average force exerted by a wall on a ball. However, it does affect the direction of the average force, which can result in a change in the ball's velocity and therefore affect the average force.

3. Is the average force exerted by a wall on a ball the same as the impact force?

No, the average force exerted by a wall on a ball is not the same as the impact force. The impact force is the force exerted by the ball on the wall, while the average force is the force exerted by the wall on the ball.

4. How does the elasticity of the ball and the wall affect the average force exerted?

The elasticity of the ball and the wall does not directly affect the average force exerted. However, it does affect the amount of time the ball takes to bounce off the wall, which can impact the calculation of the average force.

5. Can the average force exerted by a wall on a ball be negative?

Yes, the average force exerted by a wall on a ball can be negative. This would occur when the ball is moving away from the wall, resulting in a negative change in velocity and therefore a negative average force.

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