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Exam 10: Interactions and Potential Energy

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Question 31

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The potential energy for a certain mass moving in one dimension is given by U(x) = (2.0 J/m³) x³ - (15 J/m²) x² + (36 J/m) x - 23 J. Find the location(s) where the force on the mass is zero.

A) 4.0 m, 5.0 m
B) 1.0 m
C) 2.0 m, 3.0 m
D) 3.0 m, 5.0 m

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Question 32

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A ball drops some distance and gains 30 J of kinetic energy. Do NOT ignore air resistance. How much gravitational potential energy did the ball lose?

A) more than 30 J
B) exactly 30 J
C) less than 30 J

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Question 33

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A particle experiences a force given by F(x) = α - βx³. Find the potential field U(x) the particle is in. (Assume that the zero of potential energy is located at x = 0.)

A box of mass m is pressed against (but is not attached to) an ideal spring of force constant k and negligible mass, compressing the spring a distance x. After it is released, the box slides up a frictionless incline as shown in the figure and eventually stops. If we repeat this experiment with a box of mass 2m

When a particle is a distance r from the origin, its potential energy function is given by the equation U(r) = kr, where k is a constant and r = (a) What are the SI units of k? (b) Find a mathematical expression in terms of x, y, and z for the y component of the force on the particle. (c) If U = 3.00 J when the particle is 2.00 m from the origin, find the numerical value of the y component of the force on this particle when it is at the point (-1.00 m, 2.00 m, 3.00 m).

An object is attached to a hanging unstretched ideal and massless spring and slowly lowered to its equilibrium position, a distance of 6.4 cm below the starting point. If instead of having been lowered slowly the object was dropped from rest, how far then would it then stretch the spring at maximum elongation?

Which, if any, of the following statements concerning the work done by a conservative force is NOT true?

A 2.0-kg object is moving without friction along the x-axis. The potential energy curve as a function of position is shown in the figure, and the system is conservative. If the speed of the object at the origin is 4.0 m/s, what will be its speed at 7.0 m along the +x-axis?

A roller coaster of mass 80.0 kg is moving with a speed of 20.0 m/s at position A as shown in the figure. The vertical height above ground level at position A is 200 m. Neglect friction. (a) What is the total mechanical energy of the roller coaster at point A? (b) What is the total mechanical energy of the roller coaster at point B? (c) What is the speed of the roller coaster at point B? (d) What is the speed of the roller coaster at point C?

In the figure, a stunt car driver negotiates the frictionless track shown in such a way that the car is barely in contact with the track at the top of the loop. The radius of the track is 9.9 m and the mass of the car is 1800 kg. Find the magnitude of the force of the car on the track when the car is at point A. You can treat the car as a point mass.

A projectile is fired from ground level at an angle of 40.0° above horizontal at a speed of 30.0 m/s. What is the speed of the projectile when it has reached a height equal to 50.0% of its maximum height?

When an object is solely under the influence of conservative forces, the sum of its kinetic and potential energies does not change.

A box of mass m is pressed against (but is not attached to) an ideal spring of force constant k and negligible mass, compressing the spring a distance x. After it is released, the box slides up a frictionless incline as shown in the figure and eventually stops. If we repeat this experiment but instead use a spring having force constant 2k

The plot in the figure shows the potential energy of a particle, due to the force exerted on it by another particle, as a function of distance. At which of the three points labeled in the figure is the magnitude of the force on the particle greatest?

A potential energy function is given by U(x) = (3.00 J)x + (1.00 J/m²)x³. What is the force function F(x) that is associated with this potential energy function?