Particle Work and Energy - Review Problems

RP7-1) Work is energy.

RP7-2) Is work a scalar or a vector?

RP7-3) Which of the following are non-conservative forces?

RP7-4) What makes a force conservative?

RP7-5) Does friction usually do positive or negative work?

RP7-6) A force (F) performs work on a particle. Given the following situations, choose the simplest work equation that may be employed to solve for the work.

a) F is constant and parallel to the displacement.

b) F is constant and not parallel to the displacement.

c) F changes with and is not parallel to the displacement.

RP7-7) What is the work done by a force applied to a particle that is perpendicular to the displacement of the particle?

RP7-8) Kinetic energy ... (Choose all that apply.)

RP7-9) Potential energy ... (Choose all that apply.)

RP7-10) Can gravitational potential energy be negative?

RP7-11) Can elastic potential energy be negative?

RP7-12) Match the situation with the amount of work described.

Car: Your 2700-lb car broke down and you need to push it 1/2 mi back to town. How much work did you do? Assume that the road grade is fairly level and you are applying a constant horizontal force of 100 lb.

Package: You need to lift a 30-lb package from the floor to a shelf 6 feet off the ground. How much work did you do? Assume that you are applying a constant vertical force of 1.3 times the package weight.

Mosquito: A mosquito's maximum speed in air is 0.87 miles per hour and has a typical mass of 0.00007 ounces. How much work is needed to stop a mosquito traveling at its maximum speed?

Cup: A ceramic coffee cup weighing 14 ounces is accidentally dropped from a height of 4.5 ft. How much work does the force of gravity perform on this cup?

RP7-13) A car on a roller coaster rolls down the track as shown in the figure. As the cart rolls past the point illustrated in the figure, what happens to its speed and acceleration?

RP7-14) A 2-kg collar is pulled along a shaft by force P = 30 N. The direction θ of this force varies such that θ = bx, where x is in meters and b is 0.1 rad/m. Determine the work done by P from x = 0 to x = 15 m.

RP7-15) Packages are delivered to a smooth shoot via a conveyor belt. Once the packages exit the shoot they are deposited on to a rough floor (μ_k = 0.3). The packages travel along the conveyor belt at v₁ = 1 ft/s. The height of the shoot is h = 4 ft. Neglecting the size of the packages, determine the distance (d) that the packages travel along the rough floor before coming to a stop.

RP7-16) A 12-oz collar travels along a smooth curved shaft (r = 1.2 ft). It starts from rest at position A and travels down the shaft until it encounters a spring (k = 11 lb/ft). Determine the maximum compression of the spring and the normal force exerted on the collar at position B (θ = 45^o).

The following video walks you through the solution to this problem. It is suggested that you try solving the problem first and then, if you have difficulties with the solution, watch the video for help.

RP7-17) A light flywheel rotates freely on a shaft located at its center (point O). The flywheel is attached to two masses as shown in the figure. Mass A (m_A = 50 kg) is attached to the inner radius (r_i = 10 cm) of the flywheel though an inextensible rope. Mass B (m_B = 20 kg) slides along a rough horizontal surface (μ_k = 0.3) and is attached to the flywheel's outer radius (r_o = 20 cm) through an inextensible rope that winds and unwinds without slipping. If the flywheel is released from rest, calculate the wheel's angular velocity after mass B has moved 10 cm.

RP7-18) A bicyclist, starting from rest on level ground, accelerate according to the power curve shown. The cyclist reaches his cruising speed in 1 minute. If the rider and bike weigh 160 lb, determine the cruising speed. Neglect air and rolling resistance.

The following video walks you through the solution to this problem. It is suggested that you try solving the problem first and then, if you have difficulties with the solution, watch the video for help.