1990M2. a Block of Mass M Slides up the Incline Shown Above with an Initial Speed Vo In

1990M2. A block of mass m slides up the incline shown above with an initial speed vO in the position shown.

a.If the incline is frictionless, determine the maximum height H to which the block will rise, in terms of the given quantities and appropriate constants.

b.If the incline is rough with coefficient of sliding friction , determine the maximum height to which the block will rise in terms of Hand the given quantities.

A thin hoop of mass m and radius R moves up the incline shown above with an initial speed vO in the position shown.

c.If the incline is rough and the hoop rolls up the incline without slipping, determine the maximum height to which the hoop will rise in terms of H and the given quantities.

d.If the incline is frictionless, determine the maximum height to which the hoop will rise in terms of H and the given quantities.

1995M2. A particle of mass m moves in a conservative force field described by the potential energy function U(r) = a(r/b + b/r), where a and b are positive constants and r is the distance from the origin. The graph of U(r) has the following shape.

a. In terms of the constants a and b, determine the following.

i. The position ro at which the potential energy is a minimum

ii. The minimum potential energy Uo

b. Sketch the net force on the particle as a function of r on the graph below, considering a force directed away from the origin to be positive, and a force directed toward the origin to be negative.

The particle is released from rest at r = ro/2

c. In terms of Uo and m, determine the speed of the particle when it is at r = ro .

d. Write the equation or equations that could be used to determine where, if ever, the particle will again come to rest. It is not necessary to solve for this position.

e. Briefly and qualitatively describe the motion of the particle over a long period of time.

15. A conservative force has the potential energy function U(x), shown by the graph above. A particle moving in one dimension under the influence of this force has kinetic energy 1.0 joule when it is at position x1 Which of the following is a correct statement about the motion of the particle?

(A) It oscillates with maximum position x2 and minimum position x0.

(B) It moves to the right of x3 and does not return.

(C) It moves to the left of x0 and does not return.

(D) It comes to rest at either x0 or x2.

(E) It cannot reach either x0 or x2.

Questions 1617 refer to the following graph, which represents a hypothetical potential energy curve for a particle of mass m.

16. If the particle is released from rest at position ro, its speed at position 2ro is most nearly

(A)(B)(C)(D)(E)

If you know the function of potential energy for an object, U(x), how can you find an expression of the average force exerted on the body? For the average acceleration?

2003 Mech. 1.

The 100 kg box shown above is being pulled along the x-axis by a student. The box slides across a rough surface,

and its position x varies with time t according to the equation x = 0.5t3+ 2t, where x is in meters and t is in seconds.

(a) Determine the speed of the box at time t = 0.

(b) Determine the following as functions of time t.

i. The kinetic energy of the box

ii. The net force acting on the box

iii. The power being delivered to the box

(c) Calculate the net work done on the box in the interval t = 0 to t = 2 s.

(d) Indicate below whether the work done on the box by the student in the interval t = 0 to t = 2 s would be greater than, less than, or equal to the answer in part (c).

____Greater than _____Less than _____Equal to

Justify your answer.