Energy Free Response Practice Questions2009 Mech. 1.

A 3.0 kg object is moving along the x-axis in a region where its potential energy as a function of x is given as U(x) = 4.0x2, where U is in joules and x is in meters. When the object passes the point x = -0.50 m, its velocity is +2.0 m/s. All forces acting on the object are conservative.

(a) Calculate the total mechanical energy of the object.

(b) Calculate the x-coordinate of any points at which the object has zero kinetic energy.

(c) Calculate the magnitude of the momentum of the object at x = 0.60 m.

(d) Calculate the magnitude of the acceleration of the object as it passes x = 0.60 m.

Energy Free Response Practice Questions

Energy Free Response Practice Questions2008 Mech 3. (15 points)In an experiment to determine the spring constant of an elastic cord of length 0.60 m, a student hangs the cord from a rod as represented above and then attaches a variety of weights to the cord. For each weight, the student allows the weight to hanging equilibrium then measures the entire length of the cord. The data are recorded in the table below:

(a) Use the data to plot a graph of weight versus length on the axes below. Sketch a best-fit straight line through the data.

(b) Use the best-fit line you sketched in part (a) to determine an experimental value for the spring constant k of the cord.

Energy Free Response Practice Questions

The student now attaches an object of unknown mass m to the cord and holds the object adjacent to the point at which the top of the cord is tied to the rod, as represented above. When the object is released from rest, it falls 1.5m before stopping and turning around. Assume that air resistance is negligible.

(c) Calculate the value of the unknown mass m of the object.

(d) i. Calculate how far down the object has fallen at the moment it attains it maximum speed.

ii. Explain why this is the point at which the object has its maximum speed.

iii. Calculate the maximum speed of the object.

Energy Free Response Practice Questions2007:

Energy Free Response Practice Questions

Energy Free Response Practice Questions2003

Energy Free Response Practice Questions

Energy Free Response Practice Questions1995 Mech. 2A 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 constants a and b, determine the following.

i. The position r0 at which the potential energy is a minimum

ii. The minimum potential energy U0

(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.

Energy Free Response Practice QuestionsThe particle is released from rest at r = r0/2

(c) In terms of U0 and m, determine the speed of the particle when it is at r = r0

(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.

Energy Free Response Practice Questions1987 Mech #2: The following graph shows the potential energy U(x) of a particle as a function of its position x.

a) Identify all points of equilibrium for this particle.

Suppose the particle has a constant total energy of 4.0 joules, as shown by the dashed line on the graph.

b) Determine the kinetic energy of the particle at the following positionsi. x = 2.0 m

ii. x = 4.0 m

Energy Free Response Practice Questionsc) Can the particle reach the position x = 0.5 m? Explain.

d) Can the particle reach the position x = 5.0 m? Explain.

e) On the grid below, carefully draw a graph of the conservative force acting on the particle as a function of x, for 0 < x < 7 meters.

Energy Free Response Practice Questions1982 Mech. 1 A 20-kilogram mass, released from rest, slides 6 meters down a frictionless plane inclined at an angle of 30o with the horizontal and strikes a spring of spring constant k = 200 newtons per meter, as shown in the diagram below.

Assume that the spring is ideal, that the mass of the spring is negligible, and that mechanical energy is

conserved. Use g = 10 m/s2. (sin 30o = 12, cos 30o =

√32 ).

a) Determine the speed of the block just before it hits the spring.

b) Determine the distance the spring has been compressed when the block comes to rest.

c) Is the speed of the block a maximum at the instant the block strikes the spring? Justify your answer.

Energy Free Response Practice Questions

1981 Mech 2: A swing seat of mass M is connected to a fixed point P by a massless cord of length L.. A child also of mass M sits on the seat and begins to swing with zero velocity at a position at which the cord makes a 60o angle with the vertical as shown in Figure I. The swing continues down until the cord is exactly vertical at which time the child jumps off in horizontal direction. The swing continues in the same direction until the cord makes a 45o angle with the vertical as shown in figure II; at that point it begins to swing in the reverse direction. With what velocity, relative to the ground, did the child leave the swing?

(sin 45o = cos 45o =

√22 ; cos 30o = sin 60o =

√32 ; sin 30o = cos 60o =

12 )