Exam C: Energy
Name:
(Total points=100)
Signed:
PHY 161 General Physics I: Mechanics and Thermodynamics
Physics Department — Mercer University — Spring 2010
• Except for multiple choice questions, answers provided without explanation will receive little or no credit,
so you must SHOW ALL YOUR WORK.
• All answers should be decimal numbers. Please do not leave answers in terms of π, fractions, square roots,
trig functions, or inverse trig functions.
• Except as noted, provide numerical answers that are either EXACT, or accurate to THREE SIGNIFICANT
FIGURES, or WITHIN 1% of the exact answer.
• Acceleration due to gravity at the Earth’s surface: g = 9.81m/s2 .
• For all problems in this exam, ignore the effects of air resistance.
A:(30 points total, 5 points @) Multiple Choice.
Circle the letter of the correct answer(s).
1. Circle the letter for each statement that is true. [One point for each correct one.]
A) The scalar product of two vectors can be negative.
 
 
B) A ⋅ cB = c( B ⋅ A) , where c is a real number.
C) For the scalar product of two 3-component vectors (I.e., each has x, y and z.) to be non-zero, at
least two of the components of each vector must be non-zero.
  
     
D) If A = B + C , then D ⋅ A = D ⋅ B + D ⋅ C .
E) The magnitude of the sum of any two vectors equals the sum of their magnitudes.
2. Circle the letter for each statement that is true. [One point for each correct one.]
A) Friction always does negative work.
B) Potential energy may be defined by the equation U(x) = –dF(x)/dx.
C) The work done by a conservative force between two points depends on the path taken between
those points.
D) A conservative force alone cannot change a body's mechanical energy.
E) The work done by a conservative force while a body moves at constant velocity must be zero.
3. The graph below shows the potential energy of an object as a function of position.
Determine the force as a function of position in these three regions:
(-5 m < x < -2 m, -2 m < x < +1 m, +1 m < x < +5 m).
A) F(x) = (-2 N, -1 N, -1 N)
B) F(x) = (+1 N, 0 N, +2 N)
C) F(x) = (-2 N, 0 N, -1 N)
D) F(x) = (+2 N, 0 N, +1 N)
E) F(x) = (+3 N, +3 N, +4 N)
A (continued). Circle the letter of the correct answer(s).
4. An elevator is rising at constant speed. The only forces acting on it are gravity and the cable force.
Circle the letter for each statement that is true. [One point for each correct one.]
A)
B)
C)
D)
E)
The upward cable force is constant.
The upward cable force is greater than the weight of the elevator.
The gravitational potential energy of the Earth-elevator system is constant.
The kinetic energy of the elevator is constant.
The mechanical energy of the Earth-elevator system is constant.
5. The potential energy function for a system is given by U1(x) = Cx2 + Bx3. The potential energy
function for a second system is given by U2(x) = A + Cx2 + Bx3, where A is a constant energy. If both
systems begin at the same initial position with the same initial velocity, how is the motion of the two
systems related?
A) The second system will move faster if A > 0 and slower if A < 0, relative to the first system.
B) The second system will eventually move faster than the first system.
C) The second system will eventually move slower than the first system.
D) The motion of the two systems is identical.
E) The details of the motion of the second system depend on the exact value of A.
6. Three identical blocks move either on a horizontal surface, up a plane, or down a plane, as shown
below. The only forces acting on them are gravity, the normal force, and friction. They all start with
the same speed and continue to move until brought to rest by the combined effect of these forces. Rank
the three situations according to the mechanical energy dissipated by friction, from least to greatest.
A) 1, 2, 3
B) 3, 2, 1
C) 1, 3, 2
D) 2, 1, 3
E) The same for all cases