Steel ball dropped onto a plate

In summary, the problem can be solved using the impulse-momentum theorem. By calculating the speed of the ball and the depth of the dent, the momentum and impulse can be determined, allowing for the calculation of the average force exerted by the plate on the ball during impact. Comparing forces and energies is not a valid approach in this problem.
  • #1
Jacob87411
171
1
A 5.60 kg steel ball is dropped onto a copper plate from a height of 10.0 m. If the ball leaves a dent 3.10 mm deep, what is the average force exerted by the plate on the ball during the impact?

Ok so if you calculate out the speed of the ball you should get the ball is going 14 m/s when it hits the plate. Do you use Work = Force * Distance? With the distance being the amount the dent went (3.1 mm) and the force would be equal to the energy the ball has before it hits the plate? Thanks for any help/advice
 
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  • #2
In my opinion, I'll solve this problem in this way.
Consider [tex]\Delta W=W_i-W_f[/tex]
I use the equation

[tex]\Delta W=(F-P)\Delta x\Longrightarrow F=\frac{\Delta W}{\Delta x}+P[/tex]
 
  • #3
Jacob87411 said:
A 5.60 kg steel ball is dropped onto a copper plate from a height of 10.0 m. If the ball leaves a dent 3.10 mm deep, what is the average force exerted by the plate on the ball during the impact?

Ok so if you calculate out the speed of the ball you should get the ball is going 14 m/s when it hits the plate. Do you use Work = Force * Distance? With the distance being the amount the dent went (3.1 mm) and the force would be equal to the energy the ball has before it hits the plate? Thanks for any help/advice

My attack would be to use the impulse-momentum theorem. You know how fast the ball is going when it hits the copper. This allows you to calculate the momentum of the ball before impact. The momentum of the ball when it reaches the bottom of the dent is zero, so you know the change in momentum. So you can figure the impulse. Now, impulse is average force times time. You can find the time by looking at the speed of the ball at impact and the depth of the dent by kinematics. Use [tex] y=y_0 +(1/2)(v_0+v)t [/tex].

Typically, if a problem is looking for average force, the impulse-momentum theorem is a good starting point.

-Dan
 
  • #4
Jacob87411 said:
...and the force would be equal to the energy the ball has before it hits the plate?
Forces and energies are completely different quantities with different units. You can not compare or equate them.
 

What is the purpose of dropping a steel ball onto a plate in a scientific experiment?

The purpose of this experiment is to study the effects of impact and energy transfer between two objects. By dropping a steel ball onto a plate, we can observe and measure the changes in kinetic energy, potential energy, and sound energy.

What factors can affect the outcome of this experiment?

The outcome of this experiment can be affected by various factors including the height from which the ball is dropped, the mass and material of the ball, the type and thickness of the plate, and the surface on which the plate is placed.

How does the energy of the steel ball change during its impact with the plate?

As the steel ball falls and collides with the plate, its kinetic energy decreases while its potential energy increases. Upon impact, some of the energy is transferred to the plate and converted into sound energy, causing the ball to bounce back with less energy than it started with.

What is the relationship between the height of the drop and the impact force?

The impact force of the steel ball on the plate is directly proportional to the height from which it is dropped. This means that the higher the drop height, the greater the impact force and the more energy is transferred to the plate.

How can this experiment be applied in real-world scenarios?

The principles observed in this experiment can be applied in various real-world scenarios such as studying the impact of objects in collisions, designing safety equipment and structures to absorb impact energy, and analyzing the effects of earthquakes or other natural disasters on buildings and structures.

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