Question 1

Two vectors   and   are given by   and   . If these two vectors are drawn starting at the same point, what is the angle between them?

Accepted Answer

A)  106° 
B)  102° 
C)  110° 
D)  113° 
E)  97° 
A)  106° 
B)  102° 
C)  110° 
D)  113° 
E)  97°

Question 2

How much work is done by a person lifting a 2.0-kg object from the bottom of a well at a constant speed of 2.0 m/s for 5.0 s?

Accepted Answer

A)  0.22 kJ 
B)  0.20 kJ 
C)  0.24 kJ 
D)  0.27 kJ 
E)  0.31 kJ 
A)  0.22 kJ 
B)  0.20 kJ 
C)  0.24 kJ 
D)  0.27 kJ 
E)  0.31 kJ

Question 3

Two identical springs with spring constant 50 N/m support a 5.0 N weight as in the picture below. What is the change in length of each spring when the weight is hung on the springs?

Accepted Answer

A)  2.9 cm 
B)  5.0 cm 
C)  5.8 cm 
D)  7.5 cm 
E)  10.0 cm 
A)  2.9 cm 
B)  5.0 cm 
C)  5.8 cm 
D)  7.5 cm 
E)  10.0 cm

Question 4

If   = 6.0,   = 5.0, and α = 40°, determine the scalar product of the two vectors shown.

Accepted Answer

A)  +19 
B)  +23 
C)  −19 
D)  −23 
E)  +30 
A)  +19 
B)  +23 
C)  −19 
D)  −23 
E)  +30

Question 5

As a 2.0-kg object moves from   m to   m, the constant resultant force acting on it is equal to   N. If the speed of the object at the initial position is 4.0 m/s, what is its kinetic energy at its final position?

Accepted Answer

A)  62 J 
B)  53 J 
C)  73 J 
D)  86 J 
E)  24 J 
A)  62 J 
B)  53 J 
C)  73 J 
D)  86 J 
E)  24 J

Question 6

A baseball outfielder throws a baseball of mass 0.15 kg at a speed of 40 m/s and initial angle of 30°. What is the kinetic energy of the baseball at the highest point of the trajectory?

Accepted Answer

The answer of A baseball outfielder throws a baseball of...

Question 7

A 5.0-kg object is pulled along a horizontal surface at a constant speed by a 15-N force acting 20° above the horizontal. How much work is done by this force as the object moves 6.0 m?

Accepted Answer

A)  78 J 
B)  82 J 
C)  85 J 
D)  74 J 
E)  43 J 
A)  78 J 
B)  82 J 
C)  85 J 
D)  74 J 
E)  43 J

Question 8

A 2.0-kg block slides down a frictionless incline from point A to point B. A force (magnitude P = 3.0 N) acts on the block between A and B, as shown. Points A and B are 2.0 m apart. If the kinetic energy of the block at A is 10 J, what is the kinetic energy of the block at B?

Accepted Answer

A)  27 J 
B)  20 J 
C)  24 J 
D)  17 J 
E)  37 J 
A)  27 J 
B)  20 J 
C)  24 J 
D)  17 J 
E)  37 J

Question 9

The only force acting on a 1.6-kg body as it moves along the x axis is given in the figure. If the velocity of the body at x = 2.0 m is 5.0 m/s, what is its kinetic energy at x = 5.0 m?

Accepted Answer

A)  52 J 
B)  44 J 
C)  36 J 
D)  60 J 
E)  25 J 
A)  52 J 
B)  44 J 
C)  36 J 
D)  60 J 
E)  25 J

Question 10

A conservative force on a particle moving along the x axis is given by   . Which of the following is a potential that is associated with this force?

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
E)  No answer given above is correct. 
A) 
  
B) 
  
C) 
  
D) 
  
E)  No answer given above is correct.

Question 11

A constant force of 12 N in the positive x direction acts on a 4.0-kg object as it moves from the origin to the point   m. How much work is done by the given force during this displacement?

Accepted Answer

A)  +60 J 
B)  +84 J 
C)  +72 J 
D)  +48 J 
E)  +57 J 
A)  +60 J 
B)  +84 J 
C)  +72 J 
D)  +48 J 
E)  +57 J

Question 12

A 2.0-kg projectile moves from its initial position to a point that is displaced 20 m horizontally and 15 m above its initial position. How much work is done by the gravitational force on the projectile?

Accepted Answer

A)  +0.29 kJ 
B)  −0.29 kJ 
C)  +30 J 
D)  −30 J 
E)  −50 J 
A)  +0.29 kJ 
B)  −0.29 kJ 
C)  +30 J 
D)  −30 J 
E)  −50 J

Question 13

Each of two vectors,   and   , lies along a coordinate axis in the xy plane. Each vector has its tail at the origin, and the dot product of the two vectors is   . Which possibility is correct?

Accepted Answer

A) 
  and
  both lie along the positive x axis. 
B) 
  lies along the positive x axis.
  lies along the negative x axis. 
C) 
  and
  both lie along the positive y axis. 
D) 
  lies along the negative x axis.
  lies along the negative y axis. 
E) 
  lies along the positive y axis.
  lies along the negative y axis. 
A) 
  and
  both lie along the positive x axis. 
B) 
  lies along the positive x axis.
  lies along the negative x axis. 
C) 
  and
  both lie along the positive y axis. 
D) 
  lies along the negative x axis.
  lies along the negative y axis. 
E) 
  lies along the positive y axis.
  lies along the negative y axis.

Question 14

If   = 5.0,   = 8.0, and α = 30°, determine the scalar product of the two vectors shown.

Accepted Answer

A)  −35 
B)  +35 
C)  −20 
D)  +20 
E)  +40 
A)  −35 
B)  +35 
C)  −20 
D)  +20 
E)  +40

Question 15

The same constant force is used to accelerate two carts of the same mass, initially at rest, on horizontal frictionless tracks. The force is applied to cart A for twice as long a time as it is applied to cart B. The work the force does on A is WA; that on B is WB. Which statement is correct?

Accepted Answer

A)  WA = WB. 
B)  WA =
  WB. 
C)  WA = 2 WB. 
D)  WA = 4 WB. 
E)  WB = 2 WA. 
A)  WA = WB. 
B)  WA =
  WB. 
C)  WA = 2 WB. 
D)  WA = 4 WB. 
E)  WB = 2 WA.

Question 16

A 20-kg block on a horizontal surface is attached to a light spring (force constant = 8.0 kN/m). The block is pulled 10 cm to the right from its equilibrium position and released from rest. When the block has moved 2.0 cm toward its equilibrium position, its kinetic energy is 13 J. How much work is done by the frictional force on the block as it moves the 2.0 cm?

Accepted Answer

A)  −2.5 J 
B)  −1.4 J 
C)  −3.0 J 
D)  −1.9 J 
E)  −14 J 
A)  −2.5 J 
B)  −1.4 J 
C)  −3.0 J 
D)  −1.9 J 
E)  −14 J

Question 17

A 2.0-kg block sliding on a frictionless horizontal surface is attached to one end of a horizontal spring (k = 600 N/m) which has its other end fixed. The speed of the block when the spring is extended 20 cm is equal to 3.0 m/s. What is the maximum speed of this block as it oscillates?

Accepted Answer

A)  4.6 m/s 
B)  5.3 m/s 
C)  5.7 m/s 
D)  4.9 m/s 
E)  3.5 m/s 
A)  4.6 m/s 
B)  5.3 m/s 
C)  5.7 m/s 
D)  4.9 m/s 
E)  3.5 m/s

Question 18

A moving particle is subject to conservative forces only. When its kinetic energy decreases by 10 J, what happens to its mechanical energy?

Accepted Answer

A)  It increases by 10 J. 
B)  It decreases by 10 J. 
C)  It increases, but not necessarily by 10 J. 
D)  It decreases, but not necessarily by 10 J. 
E)  It remains the same. 
A)  It increases by 10 J. 
B)  It decreases by 10 J. 
C)  It increases, but not necessarily by 10 J. 
D)  It decreases, but not necessarily by 10 J. 
E)  It remains the same.

Question 19

If the scalar product of two vectors,   and   , is equal to −3.5, if   , and the angle between the two vectors when they are drawn starting from the same point is equal to 130°, what is the magnitude of   ?

Accepted Answer

A)  2.1 
B)  2.5 
C)  2.3 
D)  2.7 
E)  3.1 
A)  2.1 
B)  2.5 
C)  2.3 
D)  2.7 
E)  3.1

Question 20

An object moving along the x axis is acted upon by a force Fx that varies with position as shown. How much work is done by this force as the object moves from x = 2 m to x = 8 m?

Accepted Answer

A)  −10 J 
B)  +10 J 
C)  +30 J 
D)  −30 J 
E)  +40 J 
A)  −10 J 
B)  +10 J 
C)  +30 J 
D)  −30 J 
E)  +40 J

Exam 7: Energy of a System

Two vectors and are given by and . If these two vectors are drawn starting at the same point, what is the angle between them?

How much work is done by a person lifting a 2.0-kg object from the bottom of a well at a constant speed of 2.0 m/s for 5.0 s?

Two identical springs with spring constant 50 N/m support a 5.0 N weight as in the picture below. What is the change in length of each spring when the weight is hung on the springs?

If = 6.0, = 5.0, and α = 40°, determine the scalar product of the two vectors shown.

As a 2.0-kg object moves from m to m, the constant resultant force acting on it is equal to N. If the speed of the object at the initial position is 4.0 m/s, what is its kinetic energy at its final position?

A baseball outfielder throws a baseball of mass 0.15 kg at a speed of 40 m/s and initial angle of 30°. What is the kinetic energy of the baseball at the highest point of the trajectory?

A 5.0-kg object is pulled along a horizontal surface at a constant speed by a 15-N force acting 20° above the horizontal. How much work is done by this force as the object moves 6.0 m?

A 2.0-kg block slides down a frictionless incline from point A to point B. A force (magnitude P = 3.0 N) acts on the block between A and B, as shown. Points A and B are 2.0 m apart. If the kinetic energy of the block at A is 10 J, what is the kinetic energy of the block at B?

The only force acting on a 1.6-kg body as it moves along the x axis is given in the figure. If the velocity of the body at x = 2.0 m is 5.0 m/s, what is its kinetic energy at x = 5.0 m?

A conservative force on a particle moving along the x axis is given by . Which of the following is a potential that is associated with this force?

A constant force of 12 N in the positive x direction acts on a 4.0-kg object as it moves from the origin to the point m. How much work is done by the given force during this displacement?

A 2.0-kg projectile moves from its initial position to a point that is displaced 20 m horizontally and 15 m above its initial position. How much work is done by the gravitational force on the projectile?

Each of two vectors, and , lies along a coordinate axis in the xy plane. Each vector has its tail at the origin, and the dot product of the two vectors is . Which possibility is correct?

If = 5.0, = 8.0, and α = 30°, determine the scalar product of the two vectors shown.

The same constant force is used to accelerate two carts of the same mass, initially at rest, on horizontal frictionless tracks. The force is applied to cart A for twice as long a time as it is applied to cart B. The work the force does on A is WA; that on B is WB. Which statement is correct?

A 2.0-kg block sliding on a frictionless horizontal surface is attached to one end of a horizontal spring (k = 600 N/m) which has its other end fixed. The speed of the block when the spring is extended 20 cm is equal to 3.0 m/s. What is the maximum speed of this block as it oscillates?

A moving particle is subject to conservative forces only. When its kinetic energy decreases by 10 J, what happens to its mechanical energy?

If the scalar product of two vectors, and , is equal to −3.5, if , and the angle between the two vectors when they are drawn starting from the same point is equal to 130°, what is the magnitude of ?

An object moving along the x axis is acted upon by a force Fx that varies with position as shown. How much work is done by this force as the object moves from x = 2 m to x = 8 m?

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The same constant force is used to accelerate two carts of the same mass, initially at rest, on horizontal frictionless tracks. The force is applied to cart A for twice as long a time as it is applied to cart B. The work the force does on A is W_A; that on B is W_B. Which statement is correct?

An object moving along the x axis is acted upon by a force F_x that varies with position as shown. How much work is done by this force as the object moves from x = 2 m to x = 8 m?