Explain why or why not Determine whether the following stateme...

Question

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.

c. The work required to lift a 10-kg object vertically 10 m is the same as the work required to lift a 20-kg object vertically 5 m.

Accepted Answer

Welcome back everyone to another video. Is the work required to lift a 12 kg object 8 m vertically the same as the work required to lift a 24 kg object 4 m vertically? Use calculus to justify your answer. A says yes, and B says no. For this problem, let's recall that work done is equal to the integral of force with respect to position between two X coordinates X1 and X2. We want to understand that in this problem, force is equal to mass multiplied by the acceleration due to gravity, right, where F is the applied force, and then we can show that work is equal to the integral of M multiplied by G. D X Evaluated from X1 up to X2, both mass and G. are constants, so we can say that this is MG multiplied by the integral from X1. Up to x2 of the X. So now, let's evaluate each work, starting with work number one, which corresponds to the first object. This would be M multiplied by G. Our mass is 12. Now, G is approximately 9.8 m per second squared, but we can just use G because it's a constant, and we're integrating. D X from 0, let's suppose that our initial position is 0, and now the upper limit of integration is going to be 8, right? We got 12G. The integral of DX is simply X, and we're evaluating from 0 to 8. This is equal to 12G in 8 minus 0. Which is equal to 96 G. And the units would be jewels. Now work 2 is equal 2. What is our mass? Well, that's 24 kg. We get 24G integral from 0 to 4 because now it says 4 m vertically. And we're integrating the X. We get 24G multiplied by X, which is the integral of the X, evaluated from 0 to 4. This is equal to 24G and print C 4 minus 0, which is also 96GJules. So we can say that yes, the work is the same, which corresponds to the answer choice A. Thank you for watching.

Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
c. The work required to lift a 10-kg object vertically 10 m is the same as the work required to lift a 20-kg object vertically 5 m.

Key Concepts

Work Done by a Force

Weight and Gravitational Force

Comparing Work for Different Masses and Distances

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