Question 1

A spring with force constant k = 300 N/m is compressed 9.0 cm. What is the potential energy in the spring? A) 1.2 x 10⁴ J B) 2.4 J C) 2.7 x10⁴ J D) 27 J E) 1.2 J

Accepted Answer

The potential energy stored in a compressed spring is given by the formula $ \frac{1}{2}kx^2 $, where $ k $ is the spring constant and $ x $ is the compression distance. Here, $ k = 300 \, \text{N/m} $ and $ x = 9.0 \, \text{cm} = 0.09 \, \text{m} $. Plugging these values into the formula gives $ \frac{1}{2} \times 300 \times (0.09)^2 = 1.215 \, \text{J} $, which rounds to 1.2 J.

Question 2

The total mechanical energy of any system is
A) always the work done by gravity.
B) the difference between the kinetic and potential energy at any point.
C) the sum of the kinetic and potential energy at any point.
D) the sum of the translational and rotational kinetic energies at any point.
E) the potential energy of a spring at any displacement.

Accepted Answer

According to the law of conservation of energy, the total mechanical energy of a system, which is the sum of its kinetic energy and potential energy at any point, remains constant unless acted upon by external forces. Hence, option C is correct. Option A is incorrect because the work done by gravity is just a part of potential energy. Option B is incorrect because the difference between kinetic and potential energy may not remain constant. Options D and E are also incorrect as they do not consider the potential energy of the system.

Question 3

A 5200-kg cable car in Hong Kong is pulled a distance of 360 m up a hill inclined at 12^o from the horizontal. The change in the potential energy of the car is A) 1.8 x 10⁷ J B) 1.2 x10⁷ J C) 3.8 x10⁶ J D) 6.0 x10⁷ J E) 1.8 x 10⁶ J

Accepted Answer

The answer of A 5200-kg cable car in Hong Kong...

Question 4

Which of the following statements is NOT correct?
A) The work done by a conservative force on an object is independent on the path taken.
B) The work done by a conservative force on an object along path A$\rightarrow$B is negative that of path B$\rightarrow$A.
C) The force due to gravity is an example of a conservative force.
D) Friction is an example of a conservative force.
E) The work done by friction on an object depends on the path taken.

Accepted Answer

Friction is not an example of a conservative force. Conservative forces are those that do not depend on the path taken by the object and can be derived from a potential energy function. Friction is a non-conservative force that always opposes the direction of motion and depends on the path taken.

Question 5

A block of mass, m, is pushed up against a spring, compressing it a distance x, and is then released. The spring projects the block along a frictionless horizontal surface, giving the block a speed v. The same spring projects a second block of mass 4m, giving it a speed 3v. What distance was the spring compressed in the second case?
A) x
B) 2x
C) 3x
D) 4x
E) 6x

Accepted Answer

Let's first use the conservation of energy to find the initial compression of the spring in the first case. The potential energy stored in the spring when it's compressed by x is:

U = 1/2 k x^2

where k is the spring constant. When the block is released, all the potential energy is converted to kinetic energy:

1/2 m v^2 = U = 1/2 k x^2

Solving for x, we get:

x = sqrt(m v^2 / k)

In the second case, the same spring is used to project a block of mass 4m with speed 3v. Again, using the conservation of energy, we have:

1/2 (4m) (3v)^2 = U = 1/2 k y^2

where y is the unknown compression of the spring in the second case. We can rewrite this as:

y^2 = 36 (m/k) v^2

Now we can use the ratio of x and y to find the answer:

y/x = sqrt(36 (m/k) v^2 / (m v^2 / k))
y/x = 6

Therefore, the distance the spring was compressed in the second case is 6 times the distance in the first case, which is 3x. Hence, the answer is C) 3x.

Question 6

A projectile of mass m is propelled from ground level with kinetic energy of 450 J. At the exact top of its trajectory, its kinetic energy is 250 J. To what height above the starting point does the projectile rise?
A)  m
B)  m
C)  m
D)  m
E)  m

Accepted Answer

The answer of A projectile of mass m is propelled...

Question 7

The block shown in the figure is sliding on a frictionless surface. Its speed when it reaches the level portion of the surface on which it is sliding will be
A) 3.14 m/s
B) 7.67 m/s
C) 9.81 m/s
D) 13.3 m/s
E) 3.84 m/s

Accepted Answer

The answer of  The block shown in the figure...

Question 8

According to quantum chromodynamics, the force that keeps quarks confined within a proton or neutron) increases as the separation between the individual quarks increases. Which statement below best represents this scenario? A) The quarks are tied together by nonstretchable strings. B) The quarks are tied together by elastic strings. C) The quarks move independently of each other. D) The force between the quarks has a 1/r² behavior like gravity. E) The potential energy of a quark decreases with separation.

Accepted Answer

According to quantum chromodynamics, the force between quarks increases as they are separated, similar to how an elastic string resists stretching as it is pulled apart. Therefore, choice B, which suggests that the quarks are tied together by elastic strings, is the best representation of this scenario.

Question 9

A flexible rope of mass m and length L = L₁ + L₂, hangs over a frictionless peg, as shown in the figure. What is the speed of the rope when it just slides off the peg? A) B) C) D) E)

Accepted Answer

The answer of A flexible rope of mass m and...

Question 10

In magazine car tests an important indicator of performance is the zero to 60 mph 0 to 96.6 km/h) acceleration time. A time below 6.0 s is considered to be extremely quick. If a car with mass 1300 kg were dropped vertically from a great height, how long would it take to go from zero to 60 mph and what would the magnitude of the change in gravitational potential energy be during this time? neglect air resistance)
A) 2.74 s and 17.4 kJ
B) 2.74 s and 468 kJ
C) 2.74 s and 468 mJ
D) 0.37 s and 468 mJ
E) 2.74 s and 17.4 mJ

Accepted Answer

To find the time it takes for the car to reach 60 mph, we can use the formula for acceleration due to gravity:

v = at

where v is the final velocity (60 mph or 26.8 m/s), a is the acceleration due to gravity (9.8 m/s^2), and t is the time it takes to reach that velocity.

Rearranging the formula, we get:

t = v/a = 26.8 m/s / 9.8 m/s^2 = 2.74 s

So it takes 2.74 seconds for the car to go from zero to 60 mph.

To find the change in gravitational potential energy, we need to use the formula:

ΔPE = mgh

where m is the mass of the car (1300 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height the car falls from.

Assuming the car is dropped from rest from a great height, h is unknown, but it cancels out when we use conservation of energy:

ΔPE = ΔKE

where ΔKE is the change in kinetic energy, which we can find using:

KE = (1/2)mv^2

KE = (1/2) * 1300 kg * (26.8 m/s)^2 = 468,040 J or 468 kJ (to three significant figures)

Therefore, the magnitude of the change in gravitational potential energy is also 468 kJ, so the best answer choice is (B).

Question 11

A body falls through the atmosphere consider air resistance) gaining 20 J of kinetic energy. How much gravitational potential energy does it lose?
A) exactly 20 J
B) more than 20 J
C) less than 20 J
D) It is impossible to tell without knowing the mass of the body.
E) It is impossible to tell without knowing the displacement of the body

Accepted Answer

The body loses more than 20 J of gravitational potential energy because some energy is converted into kinetic energy (20 J), while the rest is dissipated as thermal energy due to air resistance.

Question 12

A flexible rope of mass m and length L = L₁ + L₂, hangs over a frictionless peg, as shown in the figure. What is the change in potential energy when the end of the rope just slides off the peg? A) mgL B) mgL₁ C) mgL₂ D) mgL₁²/L) E) mgL₁L₂/L)

Accepted Answer

The answer of A flexible rope of mass m and...

Question 13

Two unequal masses hang from either end of a massless cord that passes over a frictionless pulley. Which of the following is true about the change in gravitational potential energy U) and the change in kinetic energy of the system K) after the masses are released from rest? A) "$\Delta$U < 0 and $\Delta$K > 0" B) "$\Delta$U = 0 and $\Delta$K > 0" C) "$\Delta$U < 0 and $\Delta$K = 0" D) "$\Delta$U = 0 and $\Delta$K = 0" E) "$\Delta$U > 0 and $\Delta$K < 0"

Accepted Answer

The gravitational potential energy decreases ($\Delta$U < 0) as the heavier mass descends and the lighter mass ascends. The kinetic energy increases ($\Delta$K > 0) because the system starts moving from rest.

Question 14

The graph shows a plot of the gravitational potential energy U of a 1.0-kg body as a function of its height h above the surface of a planet. The acceleration due to gravity at the surface of the planet is A) 0.25 m/s² B) 9.8 m/s² C) 4.0 m/s² D) 3.0 m/s² E) 0.3 m/s²

Accepted Answer

The answer of  The graph shows a plot of...

Question 15

A woman on a bicycle traveling at 10 m/s on a horizontal road stops pedaling as she starts up a hill inclined at 3.0^o to the horizontal. If friction forces are ignored, how far up the hill does she travel before stopping? A) 5.1 m B) 30 m C) 97 m D) 10 m E) The answer depends on the mass of the woman.

Accepted Answer

The horizontal velocity of the woman remains constant because there is no friction. Therefore, the only force acting on the woman is the gravitational force which is parallel to the incline. The force perpendicular to the incline is balanced by the normal force from the incline, so it does not affect the motion. Therefore, the motion of the woman is along the incline and can be analyzed using one-dimensional kinematics.

The initial velocity of the woman is 10 m/s, and the final velocity is 0 m/s. The acceleration is due to gravity and is given by a = g sin(3.0°), where g is the acceleration due to gravity (9.81 m/s^2). The distance traveled is given by:

Δy = (v_f^2 - v_i^2) / (2 a)

Substituting the values, we get:

Δy = (0^2 - 10^2) / (2 * 9.81 * sin(3.0°)) = 96.7 m

Rounding to the nearest whole number, the answer is 97 m. Therefore, the best choice is C. The mass of the woman does not affect the motion because the acceleration due to gravity is independent of mass.

Question 16

The block shown in the figure is sliding on a frictionless surface before reaching the rough, leveled patch. If it takes the block 9.0 m to stop, what is the coefficient of kinetic friction between the block and the surface. 
A) 3.14 m/s
B) 0.33
C) 0.66
D) 3.0
E) 3.3

Accepted Answer

Since the surface is frictionless before reaching the rough patch, the initial velocity of the block would remain constant until it reaches the rough patch. The equation for the distance traveled is:

d = (1/2)at^2 + vt

Where d is the distance traveled, a is the acceleration, t is the time, and v is the initial velocity (which is constant).

At the point where the block reaches the rough patch, friction begins to act on the block causing it to decelerate. The equation for the distance traveled during the deceleration phase can be written as:

d = vt - (1/2)ft^2

Where f is the force of friction and all other variables are the same as before.

The total distance traveled by the block before coming to a stop is 9.0 meters. Therefore, we can combine the two equations above and solve for the coefficient of kinetic friction:

9.0 = (1/2)at^2 + vt + vt - (1/2)ft^2

9.0 = vt + (1/2)at^2 - (1/2)ft^2

9.0 = vt + (1/2)t(a - f)

Since the surface is frictionless, there is no force acting on the block except for gravity (which can be ignored since the surface is horizontal). Therefore, the acceleration of the block is equal to zero. Solving for the coefficient of kinetic friction yields:

f = µkN

Where µk is the coefficient of kinetic friction and N is the normal force (equal to the weight of the block). Substituting this into the equation above yields:

9.0 = vt + (1/2)t(0 - µkN)

9.0 = vt - (1/2)tµkN

µk = 2v/(9t)

Plugging in the values given in the problem (v = 6.0 m/s, t = 1.5 s) yields:

µk = 2(6.0)/(9(1.5)) = 0.33

Therefore, the coefficient of kinetic friction is 0.33, which is option B.

Question 17

Which graphbest represents kinetic energy as a function of displacement from equilibrium for a mass attached to a spring displacing from to ? 
A) 1)
B) 2)
C) 3)
D) 4)
E) 5)

Accepted Answer

The graph of kinetic energy as a function of displacement from equilibrium for a mass attached to a spring displacing from -x to x should be a symmetric parabola, with the minimum point at 0 displacement (equilibrium). Graph D is the only one that fits this description. Graphs A, B, and E have incorrect shapes, while graphs C has two minima instead of one.

Question 18

A child is sitting on the seat of a swing with ropes 10 m long. Her father pulls the swing back until the ropes make a 37^o angle with the vertical and then releases the swing. If air resistance is neglected, what is the speed of the child at the bottom of the arc of the swing when the ropes are vertical? A) 11 m/s B) 8.8 m/s C) 14 m/s D) 6.3 m/s E) 12 m/s

Accepted Answer

The answer of A child is sitting on the seat...

Question 19

Which graph best represents potential energy as a function displacement from equilibrium for a stretched spring? 
A) 1)
B) 2)
C) 3)
D) 4)
E) 5)

Accepted Answer

The answer of Which graph best represents potential energy as...

Question 20

A 75-kg man climbs the stairs to the fifth floor of a building, a total height of 16 m. His potential energy has increased by A) 1.2 x 10⁴ J B) 5.9 x10⁴ J C) 4.7 x 10⁴ J D) 3.8 x 10⁴ J E) 5.9 x10³ J

Accepted Answer

The answer of A 75-kg man climbs the stairs to...

Quiz 6: Work and Energy

A spring with force constant k = 300 N/m is compressed 9.0 cm. What is the potential energy in the spring?

The total mechanical energy of any system is

A 5200-kg cable car in Hong Kong is pulled a distance of 360 m up a hill inclined at 12o from the horizontal. The change in the potential energy of the car is

Which of the following statements is NOT correct?

A projectile of mass m is propelled from ground level with kinetic energy of 450 J. At the exact top of its trajectory, its kinetic energy is 250 J. To what height above the starting point does the projectile rise?

The block shown in the figure is sliding on a frictionless surface. Its speed when it reaches the level portion of the surface on which it is sliding will be

According to quantum chromodynamics, the force that keeps quarks confined within a proton or neutron) increases as the separation between the individual quarks increases. Which statement below best represents this scenario?

A flexible rope of mass m and length L = L1 + L2, hangs over a frictionless peg, as shown in the figure. What is the speed of the rope when it just slides off the peg?

A body falls through the atmosphere consider air resistance) gaining 20 J of kinetic energy. How much gravitational potential energy does it lose?

A flexible rope of mass m and length L = L1 + L2, hangs over a frictionless peg, as shown in the figure. What is the change in potential energy when the end of the rope just slides off the peg?

Two unequal masses hang from either end of a massless cord that passes over a frictionless pulley. Which of the following is true about the change in gravitational potential energy U) and the change in kinetic energy of the system K) after the masses are released from rest?

The graph shows a plot of the gravitational potential energy U of a 1.0-kg body as a function of its height h above the surface of a planet. The acceleration due to gravity at the surface of the planet is

A woman on a bicycle traveling at 10 m/s on a horizontal road stops pedaling as she starts up a hill inclined at 3.0o to the horizontal. If friction forces are ignored, how far up the hill does she travel before stopping?

The block shown in the figure is sliding on a frictionless surface before reaching the rough, leveled patch. If it takes the block 9.0 m to stop, what is the coefficient of kinetic friction between the block and the surface.

Which graphbest represents kinetic energy as a function of displacement from equilibrium for a mass attached to a spring displacing from to ?

Which graph best represents potential energy as a function displacement from equilibrium for a stretched spring?

A 75-kg man climbs the stairs to the fifth floor of a building, a total height of 16 m. His potential energy has increased by

A 5200-kg cable car in Hong Kong is pulled a distance of 360 m up a hill inclined at 12^o from the horizontal. The change in the potential energy of the car is

A flexible rope of mass m and length L = L₁ + L₂, hangs over a frictionless peg, as shown in the figure. What is the speed of the rope when it just slides off the peg?

A flexible rope of mass m and length L = L₁ + L₂, hangs over a frictionless peg, as shown in the figure. What is the change in potential energy when the end of the rope just slides off the peg?

A woman on a bicycle traveling at 10 m/s on a horizontal road stops pedaling as she starts up a hill inclined at 3.0^o to the horizontal. If friction forces are ignored, how far up the hill does she travel before stopping?