Question-1. A box of mass m is sliding along a horizontal surface.

Part A The box leaves position x=0 with speed v0. The box is slowed by a constant frictional force until it comes to rest at position x=x1.

Find the magnitude of the average frictional force that acts on the box. (Since you don’t know the coefficient of friction, don’t include it in your answer.)Express the frictional force in terms of m, v0, x1 Part B After the box comes to rest at position x1, a person starts pushing the box, giving it a speed v1.

When the box reaches position x2(wherex2 > x1), how much work has the person done on the box? Assume that the box reaches x2 after the person has accelerated it from rest to speedv1.Express the work in terms of m, v0, x1, x2, v1

Question-2

Understand that conservative forces can be removed from the work integral by incorporating them into a new form of energy called potential energy that must be added to the kinetic energy to get the total mechanical energy.

The first part of this problem contains short-answer questions that review the work-energy theorem. In the second part we introduce the concept of potential energy. But for now, please answer in terms of the work-energy theorem.(PART-A to PART E)

Question-3.

Part A Consider a uniform gravitational field (a fair approximation near the surface of a planet). Find U(yf)−U(y0)=−∫yfy0F⃗ g⋅ds⃗ , where F⃗ g=−mgj^ and ds⃗ =dyj^. Express your answer in terms of m, g, y0, and yf. U(yf)−U(y0) = SubmitHintsMy AnswersGive UpReview Part Part B Consider the force exerted by a spring that obeys Hooke’s law. Find U(xf)−U(x0)=−∫xfx0F⃗ s⋅ds⃗ , where F⃗ s=−kxi^,ds⃗ =dxi^, and the spring constant k is positive. Express your answer in terms of k, x0, and xf. U(xf)−U(x0) = SubmitHintsMy AnswersGive UpReview Part Part C Finally, consider the gravitational force generated by a spherically symmetrical massive object. The magnitude and direction of such a force are given by Newton’s law of gravity: F⃗ G=−Gm1m2r2r^, where ds⃗ =drr^; G, m1, and m2 are constants; and r>0. Find U(rf)−U(r0)=−∫rfr0F⃗ G⋅ds⃗ . Express your answer in terms of G, m1, m2, r0, and rf. U(rf)−U(r0) = SubmitHintsMy AnswersGive UpReview Part

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