Solutions to Practice Problems
1 . E— The force of gravity is straight down and equal to 100 N. The displacement parallel to this force
is the vertical displacement, 2.5 m. Work equals force times parallel displacement, 250 J.
2 . E— The force of friction acts up the plane, and displacement is down the plane, so just multiply force
times distance to get 50 J. The negative sign indicates that force is opposite displacement.
3 . D— Think of Chris on a skateboard—on this graph, he will oscillate back and forth about x = 0.
Because he starts with a KE of 10 J, he can, at most, have a potential energy of 10 J, which
corresponds on the graph to a maximum displacement of 5 cm. (The mass cannot have constant
acceleration because constant acceleration only occurs for a constant force; a constant force produces
an energy graph that is linear. The mass will not come to rest because we are assuming a conservative
force, for which KE can be converted to and from PE freely.)
4 . E— Kinetic energy is a scalar, so even though the balls move in opposite directions, the KEs cannot
cancel. Instead, kinetic energy ½(1 kg)(6 m/s)^2 attributable to different objects adds together
algebraically, giving 36 J total.5 . (a) The car started from rest, or zero KE. The car ended up with ½(1500 kg)(40 m/s)^2 = 1.2 × 10^6 J of
kinetic energy. So its change in KE is 1.2 × 10^6 J.
(b) The acceleration is not constant. We know that because the velocity–time graph is not linear.
(c) The distance traveled is found from the area under the graph. It is easiest to approximate by
counting boxes, where one of the big boxes is 10 m. There are, give-or-take, 19 boxes underneath
the curve, so the car went 190 m.
(d) We cannot use work = force × distance here, because the net force is continually changing (because
acceleration is changing). But Wnet = ΔKE is always valid. In part (a) the car’s change in KE was
found to be 1.2 × 10^6 J; so the net work done on the car is also 1.2 × 10^6 J.
(e) Power is work divided by time, or 1.2 × 10^6 J/7 s = 170 kW. This can be compared to the power of
a car, 220 horsepower.Rapid Review
• Energy is the ability to do work. Both energy and work are scalars.
• The work done on an object (or by an object) is equal to that object’s change in kinetic energy.
• Potential energy is energy of position, and it comes in a variety of forms; for example, there’s
gravitational potential energy and spring potential energy.
• The energy of a closed system is conserved. To solve a conservation of energy problem, start by
writing K i + Ui + W = K f + Uf , where “i ” means “initial,” “f ” means “final,” and W is the work done
by friction or an externally applied force. Think about what type of U you’re dealing with; there might
even be more than one form of U in a single problem!
• Power is the rate at which work is done, measured in watts. Power is equal to work/time , which is
equivalent to force multiplied by velocity.
• If the functional form of a conservative force is known, then the potential energy attributable to that
force is given by