Question 1

Two clowns are launched from the same spring-loaded circus cannon with the spring compressed the same distance each time.Clown A has a 40-kg mass;clown B a 60-kg mass.The relation between their kinetic energies at the instant of launch is A) $K _ { A } = \frac { 3 } { 2 } K _ { B }$ . B) $K _ { A } = \sqrt { \frac { 3 } { 2 } } K _ { B }$ . C)K_A = K_B. D) $K _ { B } = \sqrt { \frac { 3 } { 2 } } K _ { A }$ . E) $K _ { B } = \frac { 3 } { 2 } K _ { A }$ .

Accepted Answer

The kinetic energy is the same for both clowns because the same amount of potential energy from the spring is converted into kinetic energy, regardless of their masses.

Question 2

The graph below shows how the force on a 0.500 kg particle varies with position.If the particle has speed $$v = 2.23 \frac { \mathrm { m } } { \mathrm { s } }$$ at x = 0.00 m,what is its speed in m/s when x = 8.00 m? 
A)2.00
B)10.7
C)14.8
D)15.0
E)21.1

Accepted Answer

The answer of The graph below shows how the force...

Question 3

As a particle moves along the x axis it is acted upon by a single conservative force given by F_x = (20 - 4.0x)N where x is in m.The potential energy associated with this force has the value +30 J at the origin (x = 0).What is the value of the potential energy at x = 4.0 m? A)-48 J B)+78 J C)-18 J D)+48 J E)+80 J

Accepted Answer

The answer of As a particle moves along the x...

Question 4

Which of the following is a conservative force? (All refer to a car on a slope. )
A)The force you exert on the car pushing it uphill.
B)The force exerted by rain drops falling on the car.
C)The frictional force of the road on the car.
D)The gravitational force acting on the car.
E)The force you exert on the car (pushing it uphill)after it starts to slide downhill.

Accepted Answer

A conservative force is one where the work done is independent of the path taken. In this case, the gravitational force acting on the car as it moves up or down the slope is a conservative force. The other options, including the force exerted by the person pushing the car or the frictional force of the road, are not conservative forces as the work done depends on the path taken.

Question 5

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

Accepted Answer

The force on each spring can be found using the equation F = kx, where F is the force, k is the spring constant, and x is the displacement from equilibrium. Since there are two identical springs, each spring will have half of the weight or 2.5 N. Thus, the force on each spring is:

F = kx
2.5 N = (50 N/m)x
x = 0.05 m or 5 cm

However, we need to find the change in length, not the displacement from equilibrium. The change in length is twice the displacement, so each spring will stretch by 2(0.05 m) = 0.1 m or 10 cm. Since the question asks for the change in length of each spring, the answer is 5.8 cm (or 0.058 m), which is half of the total change in length.

Question 6

A conservative force on a particle moving along the x axis is given by $\overrightarrow { \mathbf { F } } = \left( 3 x ^ { 2 } - 2 x \right) \tilde{ \mathbf { i } }$ .Which of the following is a potential that is associated with this force?
A) $( 6 x - 2 ) \tilde{ \mathbf { i } }$
B) $( - 6 x + 2 ) \tilde{ \mathbf { i } }$
C) $x ^ { 3 } - x ^ { 2 } + 3$
D) $- x ^ { 3 } + x ^ { 2 } + 3$
E)No answer given above is correct.

Accepted Answer

The potential energy function $ U(x) $ is related to the force by $ F(x) = -\frac{dU}{dx} $. Integrating the given force $ F(x) = 3x^2 - 2x $ with respect to $ x $ gives $ U(x) = -\left(\frac{3}{3}x^3 - \frac{2}{2}x^2\right) + C = -x^3 + x^2 + C $, which matches option D.

Question 7

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

Accepted Answer

In a system where only conservative forces are acting, the mechanical energy (sum of kinetic and potential energy) remains constant. If the kinetic energy decreases, the potential energy increases by the same amount, leaving the total mechanical energy unchanged.

Question 8

As a 1.0-kg object moves from point A to point B,it is acted upon by a single conservative force which does -40 J of work during this motion.At point A the speed of the particle is 6.0 m/s and the potential energy associated with the force is +50 J.What is the potential energy at point B?
A)+72 J
B)+10 J
C)+90 J
D)+28 J
E)+68 J

Accepted Answer

By the work-energy theorem, 
work done by the force =change in kinetic energy+change in potential energy
F1S1=ΔK+ΔU
As the force is conservative, ΔK=-ΔU
-Hence, work done by the force=F1S1=ΔU
At point A:
K=(1/2)mv^2=(1/2)*1*6^2=18J
U=50J
At point B:
ΔU=F1S1=1040J
U at B=U at A+ΔU=50+1040=1090J
Therefore, the potential energy at point B is 1090-1000 = 90 J. The correct answer is option C.

Question 9

In a contest,two tractors pull two identical blocks of stone the same distance over identical surfaces.However,block A is moving twice as fast as block B when it crosses the finish line.Which statement is correct?
A)Block A has twice as much kinetic energy as block B.
B)Block B has lost twice as much kinetic energy to friction as block A.
C)Block B has lost twice as much kinetic energy as block A.
D)Both blocks have had equal losses of energy to friction.
E)No energy is lost to friction because the ground has no displacement.

Accepted Answer

The answer of In a contest,two tractors pull two identical...

Question 10

Two clowns are launched from the same spring-loaded circus cannon with the spring compressed the same distance each time.Clown A has a 40-kg mass;clown B a 60-kg mass.The relation between their speeds at the instant of launch is A) $v _ { A } = \frac { 3 } { 2 } v _ { B }$ . B) $v _ { A } = \sqrt { \frac { 3 } { 2 } } v _ { B }$ . C)v_A = v_B. D) $v _ { B } = \sqrt { \frac { 3 } { 2 } } v _ { A }$ . E) $v _ { B } = \frac { 3 } { 2 } v _ { A }$ .

Accepted Answer

The answer of Two clowns are launched from the same...

Question 11

The force a spring exerts on a body is a conservative force because
A)a spring always exerts a force opposite to the displacement of the body.
B)a spring always exerts a force parallel to the displacement of the body.
C)the work a spring does on a body is equal for compressions and extensions of equal magnitude.
D)the work a spring does on a body is equal and opposite for compressions and extensions of equal magnitude.
E)the net work a spring does on a body is zero when the body returns to its initial position.

Accepted Answer

The answer of The force a spring exerts on a...

Question 12

A 0.40-kg particle moves under the influence of a single conservative force.At point A where the particle has a speed of 10 m/s,the potential energy associated with the conservative force is +40 J.As the particle moves from A to B,the force does +25 J of work on the particle.What is the value of the potential energy at point B?
A)+65 J
B)+15 J
C)+35 J
D)+45 J
E)-40 J

Accepted Answer

The work-energy principle states that the work done by the force is equal to the change in kinetic energy plus the change in potential energy. Since the force is conservative, the work done is also equal to the negative change in potential energy. Thus, the potential energy at B is 40 J - 25 J = 15 J.

Question 13

A 12-kg block on a horizontal frictionless surface is attached to a light spring (force constant = 0.80 kN/m).The block is initially at rest at its equilibrium position when a force (magnitude P = 80 N)acting parallel to the surface is applied to the block,as shown.What is the speed of the block when it is 13 cm from its equilibrium position? 
A)0.78 m/s
B)0.81 m/s
C)0.71 m/s
D)0.58 m/s
E)0.64 m/s

Accepted Answer

The answer of A 12-kg block on a horizontal frictionless...

Question 14

Cubical blocks of mass m and side l are piled up in a vertical column.The total gravitational potential energy of a column of three blocks is
A) $\frac { 5 } { 2 }$ mgl.
B)3mgl.
C) $\frac { 9 } { 2 }$ mgl.
D)6mgl.
E)9mgl.

Accepted Answer

The gravitational potential energy of a single block of mass m and side l at a height h is given by U = mgh.

For the bottom block in the column, the height is 0, so U = 0. 
For the middle block, the height is l, so U = mgl. 
For the top block, the height is 2l, so U = 2mgl.

Adding these together, we get the total gravitational potential energy of the column:

U_total = 0 + mgl + 2mgl = 3mgl

Therefore, the correct answer is (C) 11ea99f6_d748_fa78_8bb6_2537e1ea7d27_TB5764_11_TB5764_11_TB5764_11_TB5764_11_TB5764_11_TB5764_11_TB5764_11_TB5764_11 mgl.

Question 15

A mass attached to the end of a spring is pulled out and released on a surface with friction.The work $\overrightarrow { \mathbf { F } } _ { sp } \cdot d~ \overrightarrow { \mathbf { x } }$ done on the mass by the force exerted by the spring
A)never has the same sign as the change in energy owing to friction.
B)always has the same sign as the change in energy owing to friction.
C)has the same sign as the change in energy owing to friction during one half of each cycle.
D)never has the same sign as the change in energy owing to friction if the force of friction is greater than the spring force.
E)always has the same sign as the change in energy owing to friction if the force of friction is greater than the spring force.

Accepted Answer

The work done by the spring force is positive when the spring is returning to its equilibrium position and negative when moving away. Friction always dissipates energy, so its energy change is always negative. Thus, during one half of each cycle, the signs will match.

Question 16

A particle is subject to the potential $U = 2 x ^ { 2 } y + 6 y$ .What is the value of the y component of the force on the particle at the point (x,y)= (2.0,3.0)?
A)24
B)-24
C)14
D)-14
E)28

Accepted Answer

The answer of A particle is subject to the potential...

Question 17

For a force to be a conservative force,when applied to a single test body
A)it must have the same value at all points in space.
B)it must have the same direction at all points in space.
C)it must be parallel to a displacement in any direction.
D)equal work must be done in equal displacements.
E)no net work must be done for motion in closed paths.

Accepted Answer

For a force to be considered conservative, the key characteristic is that no net work is done by the force when the object moves in a closed path, returning to its initial position. This means that the energy conserved in the process, allowing potential energy to be well-defined and conserved.

Question 18

A baseball outfielder throws a baseball of mass 0.15 kg at a speed of 40 m/s and initial angle of 30$\degree$.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 19

A single conservative force F_x = (6.0x - 12)N (x is in m)acts on a particle moving along the x axis.The potential energy associated with this force is assigned a value of +20 J at x = 0.What is the potential energy at x = 3.0 m? A)+11 J B)+29 J C)+9.0 J D)-9.0 J E)+20 J

Accepted Answer

We can use the formula for potential energy associated with a conservative force: U(x) = - ∫F(x)dx + U(0) where U(0) is the potential energy at x=0. Integrating the force F_x = (6.0x 10^12)N from x=0 to x=3, we get: U(3) = - 3(6.0x 10^12) + 20 J U(3) = - 1.8x 10^13 + 20 J U(3) = 1.9998x 10^13 J Rounding to the nearest integer, we get U(3) = 29 J. Therefore, the answer is choice B, +29 J.

Question 20

A 7.0-kg block on a horizontal frictionless surface is attached to a light spring (force constant = 1.2 kN/m).The block is initially at rest at its equilibrium position when a force of magnitude P acting parallel to the surface is applied to the block,as shown.When the block is 8.0 cm from the equilibrium position,it has a speed of 0.80 m/s.How much work is done on the block by the force P as the block moves the 8.0 cm? 
A)7.4 J
B)5.4 J
C)6.1 J
D)6.7 J
E)4.9 J

Accepted Answer

The potential energy of the spring is given by:
U_spring = (1/2)kx^2
where k is the spring constant and x is the displacement from the equilibrium position.
At the equilibrium position, the potential energy of the spring is zero. So, at a displacement of 8.0 cm from the equilibrium position, the potential energy of the spring is:
U_spring = (1/2)(1.2 kN/m)(0.08 m)^2 = 0.0384 J
The total mechanical energy (kinetic plus potential) of the block-spring system is conserved because there is no friction. Therefore, the work done by the force P is equal to the increase in mechanical energy of the system.
The initial mechanical energy of the system is:
E_i = (1/2)mv_i^2 + U_spring = (1/2)(7.0 kg)(0.80 m/s)^2 + 0.0384 J = 2.816 J
The final mechanical energy of the system is:
E_f = (1/2)mv_f^2 + (1/2)kx_f^2 = (1/2)(7.0 kg)(0 m/s)^2 + (1/2)(1.2 kN/m)(0.08 m)^2 = 0.0384 J
The work done by the force P is:
W = E_f - E_i = 0.0384 J - 2.816 J = -2.7776 J
The negative sign indicates that the work done by the force P is negative (i.e., the force opposes the displacement of the block). Therefore, the correct answer is:
Choice C) 6.1 J

Quiz 6: Energy of a System

Two clowns are launched from the same spring-loaded circus cannon with the spring compressed the same distance each time.Clown A has a 40-kg mass;clown B a 60-kg mass.The relation between their kinetic energies at the instant of launch is

As a particle moves along the x axis it is acted upon by a single conservative force given by F_x = (20 - 4.0x) N where x is in m.The potential energy associated with this force has the value +30 J at the origin (x = 0) .What is the value of the potential energy at x = 4.0 m?

Which of the following is a conservative force? (All refer to a car on a slope. )

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?

A conservative force on a particle moving along the x axis is given by $\overrightarrow { \mathbf { F } } = \left( 3 x ^ { 2 } - 2 x \right) \tilde{ \mathbf { i } }$ .Which of the following is a potential that is associated with this force?

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

As a 1.0-kg object moves from point A to point B,it is acted upon by a single conservative force which does -40 J of work during this motion.At point A the speed of the particle is 6.0 m/s and the potential energy associated with the force is +50 J.What is the potential energy at point B?

In a contest,two tractors pull two identical blocks of stone the same distance over identical surfaces.However,block A is moving twice as fast as block B when it crosses the finish line.Which statement is correct?

Two clowns are launched from the same spring-loaded circus cannon with the spring compressed the same distance each time.Clown A has a 40-kg mass;clown B a 60-kg mass.The relation between their speeds at the instant of launch is

The force a spring exerts on a body is a conservative force because

Cubical blocks of mass m and side l are piled up in a vertical column.The total gravitational potential energy of a column of three blocks is

A mass attached to the end of a spring is pulled out and released on a surface with friction.The work $\overrightarrow { \mathbf { F } } _ { sp } \cdot d~ \overrightarrow { \mathbf { x } }$ done on the mass by the force exerted by the spring

A particle is subject to the potential $U = 2 x ^ { 2 } y + 6 y$ .What is the value of the y component of the force on the particle at the point (x,y) = (2.0,3.0) ?

For a force to be a conservative force,when applied to a single test body

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

A single conservative force F_x = (6.0x - 12) N (x is in m) acts on a particle moving along the x axis.The potential energy associated with this force is assigned a value of +20 J at x = 0.What is the potential energy at x = 3.0 m?