How far the peg is driven into the ground due to impact?

In summary, a wooden peg with a mass of 0.4kg is hit vertically by a mallet with a mass of 2kg and a speed of 6.67m/s. The ground opposes the motion with a force of 1kN. To find how far the peg is driven into the ground, you can calculate the distance it takes for the peg to stop using the formula F=ma and the given values. Alternatively, you can also use the concept of kinetic energy and the work done by the ground to find the distance traveled.
  • #1
Gughanath
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a wooden peg is hit vertically by a mallet which is also moving vertically. The mass of the peck is 0.4kg and the mallet is 2kg. The speed at which the peg starts to move into the ground is 6.67m/s. Given that the ground opposes the motion of the peck with a force of 1kN, find how far the peg is driven into the ground due to impact? Please help me on this one??
 
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  • #2
Think of it as a mass of 2.4 Kg traveling at 6.67m/s, decelerating at a rate which you can derive from F=ma as it drives into the ground. Calculate the distance for the object to stop.

If you calculate the acelleration the force of the ground gives, you can ask a simpler question by working backwards a bit ; At a=2.77917 ms-2 what distance is traveled to reach 6.67 m/s

:edit to clarify post:
 
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  • #3
Wouldn't it be simple to use kinetic energy. The peck has some kinetic energy and the ground does negative work to the peck with a force of 1kN. Just find when the kinetic energy equals the work done by the ground.
 

FAQ: How far the peg is driven into the ground due to impact?

How does the speed of impact affect the depth the peg is driven into the ground?

The speed of impact has a significant effect on the depth the peg is driven into the ground. The higher the speed, the deeper the peg will be driven due to the greater amount of force exerted on the ground.

Does the type of surface affect the depth the peg is driven into the ground?

Yes, the type of surface can have an impact on the depth the peg is driven into the ground. Softer surfaces, such as sand or mud, will result in the peg being driven deeper compared to harder surfaces like concrete or asphalt.

Is there a correlation between the weight of the object hitting the peg and the depth it is driven into the ground?

Yes, there is a correlation between the weight of the object and the depth the peg is driven into the ground. Heavier objects will result in a deeper impact due to the increased force exerted on the ground.

How does the angle of impact affect the depth of the peg?

The angle of impact can have a significant effect on the depth the peg is driven into the ground. A steeper angle of impact will result in a deeper penetration, while a shallower angle may cause the peg to bounce off the surface and not penetrate as deep.

What other factors besides speed and weight can affect the depth the peg is driven into the ground?

Other factors that can affect the depth the peg is driven into the ground include the shape of the object (a pointed object will penetrate deeper than a flat object), the density of the surface material, and the moisture content of the ground. Wind and air resistance can also play a role in the impact force and therefore affect the depth of penetration.

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