A pile driver lifts a 250 kg weight and then lets it fall onto the end of a steel pipe that needs to be driven into the ground. A fall from an initial height of 1.5 m drives the pipe in 35 cm. What is the average force that the weight exerts on the pipe?

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Hello, everyone. Let's go through this practice problem. A construction worker drops a 2 kg hammer from the top of a building which is 40 m tall. The hammer strikes a pile driver that is resting on the ground and the pile driver drives a steel beam into the ground. If the beam is driven 25 centimeters into the ground by the impact, what is the magnitude of the average force that the hammer exerts on the pile driver option? A 3.16 new ones. B 3.16 kg newtons C 2.16 konu ones or D 2.16 new ones. So this is a problem that revolves around energy. Gravity is doing work on the hammer as the hammer falls from the top of the building and continues to do work on the hammer as it hits the beam and drives it partially into the ground. Not only is the gravity doing work on the hammer, but while the hammer is in contact with the beam, the hammer is doing work on the beam. The key thing to understand with this problem is that the energy that has been used to drive the beam into the ground comes entirely from the energy that the hammer has from as it's falling. Think about it in terms of the law of conservation of energy, which states that energy cannot be created or destroyed. Assuming this is an isolated system where we're not considering external forces that could introduce or absorb energy from the system. Then the total amount of energy in the system is the same as the hammer's potential energy before it begins falling. And we'll assume that all of that energy is being converted into the work used to drive the beam into the ground. So we can say that the work done by gravity on the hammer which I'll call W sub G is equal in magnitude to the work done by the hammer on the beam which I'll call W sub H. Recall that in general work is equal to force multiplied by the distance over which that force has been exerted. So let's apply that formula to the work equation that we've set up on the left side. So for the gravitational force recall that gravitational force is equal to mass multiplied by the acceleration due to gravity. So the, the work that gravity does on the hammer is going to be equal to the mass of the hammer multiplied by the acceleration due to gravity. And then according to our work formula, we now have to multiply this by the distance over which gravity is doing work on the hammer. This is going to be equal to the 40 m of the height of the building. Plus the additional 25 centimeters from as the hammer is driving the beam into the ground. So plus 25 centimeters or plus 2.5 or plus 0.25 m, this is equal to the work done by the hammer which again force multiplied by distance. So this is the force that the hammer exerts on the driver, which is the variable we're trying to find multiplied by the distance which is given as 25 centimeters or 0.25 m. Remember that the problem is asking us to find F sub H. So let's do some algebra by dividing both sides of the equation by 0.25 m mg multiplied by 40.25 m divided by 0.25 m. Now we'll just plug in the values that were given to us in the problem. The mass of the hammer is 2 kg. Gravitational acceleration is 9.81 m per second squared multiplied by 40.25 m. And we divide the whole thing by 0.25 m. We put this into a calculator and the force is equal to about 3155.6 new ones, which we can round with a unit prefix to approximate it as 3.16 kg. And that is our answer to this problem. Which you'll notice corresponds with option B. So option B is our answer and that is it for this problem. I hope this video helped you out and please consider checking out our other tutoring videos which will give you more experience with these types of problems. That's all for now. And I hope you have a lovely day. Bye bye.

A pile driver lifts a 250 kg weight and then lets it fall onto the end of a steel pipe that needs to be driven into the ground. A fall from an initial height of 1.5 m drives the pipe in 35 cm. What is the average force that the weight exerts on the pipe?

Verified Solution

Key Concepts

Gravitational Potential Energy

Kinetic Energy and Impact Force

Newton's Second Law of Motion