Question 1

A 1 300-kg automobile moving at 21 m/s has the brakes applied with a deceleration of 3.0 m/s².How far does the car travel before it stops? A)7.4E+1 m B)1.5E+2 m C)2.9E+5 m D)2.3E+4 m E)4.3E+2 m

Accepted Answer

To find the stopping distance, we can use the formula $d = \frac{v^2}{2a}$, where $v = 21 \, \text{m/s}$ is the initial velocity, and $a = 3.0 \, \text{m/s}^2$ is the deceleration. Plugging in the values, we get $d = \frac{(21)^2}{2 \times 3} = \frac{441}{6} = 73.5 \, \text{m}$, which is approximately $7.4 \times 10^1 \, \text{m}$.

Question 2

What is the minimum amount of energy required for a 60.0-kg climber carrying a 18-kg pack to climb Mt.Everest,8 250 m high?
A)6.3E+6 J
B)3.4E+6 J
C)4.9E+6 J
D)6.4E+5 J
E)3.5E+5 J

Accepted Answer

The minimum amount of energy required is calculated using the formula for gravitational potential energy: $E = mgh$, where $m$ is the total mass (climber + pack), $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$), and $h$ is the height climbed. Thus, $E = (60.0 \, \text{kg} + 18.0 \, \text{kg}) \times 9.8 \, \text{m/s}^2 \times 8250 \, \text{m} = 7.668 \times 10^6 \, \text{J}$, which rounds to $6.3 \times 10^6 \, \text{J}$ or $6.3E+6 \, \text{J}$.

Question 3

Which of the following is not true about potential energy?
A)Potential energy is stored energy.
B)Potential energy is related to position.
C)Potential energy is a scalar quantity.
D)Potential energy has direction.

Accepted Answer

Potential energy is a scalar quantity, which means it has only magnitude and no direction associated with it. The other choices are true statements about potential energy.

Question 4

A 8.00-kg bowling ball falls from a 3.50-m shelf.Just before hitting the floor,what will be its kinetic energy? (g = 9.80 m/s² and assume air resistance is negligible) A)280 J B)49.0 J C)2.86 J D)274 J E)28.0 J

Accepted Answer

Potential energy before falling can be calculated using the formula:
PE = mgh = 8.00 kg x 9.80 m/s^2 x 3.50 m = 274.4 J

At the moment just before hitting the floor, all of this potential energy is converted to kinetic energy:
KE = 274.4 J

Therefore, the correct answer is D) 274 J

Question 5

A 1.00-kg ball has zero kinetic and potential energy.Ernie drops the ball into a 10.0-m-deep well.Just before the ball hits the bottom,the sum of its kinetic and potential energy is:
A)zero.
B)98.0 J.
C)−98.0 J.
D)196 J.
E)−196 J.

Accepted Answer

The ball has zero kinetic and potential energy at the top of the well. As it falls, it gains kinetic energy and loses potential energy. Just before it hits the bottom, all of its energy is kinetic energy, which is equal to its potential energy at the top of the well. Therefore, the sum of its kinetic and potential energy is zero.

Question 6

Jasper takes two books of mass m₁ and m₂ off the floor and places them on a shelf at height h.The change in potential energy of the book with mass m₁ is four times that of the book with mass m₂.What is the relationship between m₁ and m₂? A)m1 = 0.25m₂ B)m1 = 0.5m₂ C)m1 = 2m₂ D)m1 = 4m₂

Accepted Answer

The change in potential energy (ΔPE) is given by ΔPE = mgh, where m is mass, g is the acceleration due to gravity, and h is the height. If the change in potential energy of the first book is four times that of the second book, and both are raised to the same height, then their masses must be in the same ratio because g and h are constants. Therefore, m1 = 4m2.

Question 7

A professional skier reaches a speed of 58.0 m/s on a 30° ski slope.Ignoring friction,what was the minimum distance along the slope the skier would have had to travel,starting from rest?
A)172 m
B)198 m
C)343 m
D)5.92 m
E)0.291 m

Accepted Answer

Using the equations of motion where v is final velocity, u is initial velocity, a is acceleration and s is distance travelled:

v^2 = u^2 + 2as

We are given that the initial velocity, u is 0 m/s, final velocity, v is 58.0 m/s, angle of slope, θ is 30 degrees and acceleration, a is acceleration due to gravity, g which is approximately 9.81 m/s^2.

Let's convert θ to radians:

θ = 30 degrees = π/6 radians

Now we can calculate the minimum distance, s using the above equation:

58.0^2 = 0^2 + 2(9.81)s(sin π/6)

s = (58.0^2)/(2*9.81*sin π/6) = 342.6 m ≈ 343 m (to three significant figures)

Therefore, the minimum distance along the slope the skier would have had to travel, starting from rest is 343 m. The answer is (C).

Question 8

A horizontal force of 200 N is applied to a 55.0-kg cart across a 15.0-m level surface.If the cart accelerates at 2.0 m/s²,then what is the work done by the force of friction as it acts to retard the motion of the cart? A)-4.7E+3 J B)-1.4E+3 J C)-3.0E+3 J D)-9.0E+1 J E)-3.1E+2 J

Accepted Answer

The net force on the cart is given by F_net = mass * acceleration = 55 kg * 2 m/s² = 110 N. The applied force is 200 N, so the force of friction is 200 N - 110 N = 90 N. The work done by friction is W = force * distance * cos(θ), where θ = 180° since friction opposes motion, so W = 90 N * 15 m * (-1) = -1350 J, which is approximately -1.4E+3 J.

Question 9

A boat with mass 950 kg is heading into the harbor at a speed of 10.0 m/s.How much work is required to slow the boat to 1.0 m/s?
A)4.8E+4 J
B)9.4E+4 J
C)4.7E+4 J
D)2.3E+4 J

Accepted Answer

The answer of A boat with mass 950 kg is...

Question 10

A rock is thrown straight up with an initial velocity of 15.0 m/s.Ignore energy lost to air friction.How high will the rock rise?
A)7.5 m
B)113 m
C)23.0 m
D)11.5 m
E)0.0871 m

Accepted Answer

The maximum height can be calculated using the formula $ h = \frac{v^2}{2g} $, where $ v = 15.0 \, \text{m/s} $ and $ g = 9.8 \, \text{m/s}^2 $. Plugging in the values, $ h = \frac{(15.0)^2}{2 \times 9.8} = 11.5 \, \text{m} $.

Question 11

A boat with mass of 1 200 kg is traveling at 12 m/s.What is the magnitude of the force required to stop the boat if it undergoes a displacement of 85 m?
A)2 000 N
B)170 N
C)8 500 N
D)1 000 N

Accepted Answer

The answer of A boat with mass of 1 200...

Question 12

Samantha pushes a 60-N crate up a ramp 30 m in length and inclined at 10° with the horizontal.What potential energy change does the crate experience?
A)1.8E+3 J.
B)1.8E+3 J
C)1.2E+1 J
D)3.1E+2 J
E)1.0E+4 J

Accepted Answer

The answer of Samantha pushes a 60-N crate up a...

Question 13

A golf ball hits a wall and bounces back at 3/4 the original speed.What part of the original kinetic energy of the ball did it lose in the collision?
A)1/4
B)3/8
C)7/16
D)9/16
E)​3/4

Accepted Answer

The kinetic energy (KE) of an object is given by the formula KE = 1/2 mv^2, where m is the mass of the object and v is its velocity. If the ball bounces back at 3/4 of its original speed, its new kinetic energy is KE_new = 1/2 m (3/4v)^2 = 1/2 m (9/16)v^2 = 9/16 KE_original. Therefore, the ball loses 1 - 9/16 = 7/16 of its original kinetic energy in the collision.

Question 14

A 6.1-g bullet has a velocity of 475 m/s when it penetrates a wooden door to a depth of 3.5 cm.Assuming the frictional force that stops the bullet is constant,how long does it take from the time the bullet hits the door till it comes to a stop?
A)1.5E-4 s
B)7.4E-5 s
C)4.5E-2 s
D)3.7E-3 s

Accepted Answer

The answer of A 6.1-g bullet has a velocity of...

Question 15

A 10.0-kg box starts at rest and slides 3.90 m down a ramp inclined at an angle of 10° with the horizontal.If there is no friction between the ramp surface and crate,what is the velocity of the crate at the bottom of the ramp? (g = 9.8 m/s²) A)13.3 m/s B)3.64 m/s C)8.74 m/s D)8.68 m/s E)76.4 m/s

Accepted Answer

The potential energy at the top of the ramp is equal to the kinetic energy at the bottom, since there is no friction. So,
mgh = 1/2mv^2
where m = 10.0 kg, h = 3.90 m sin(10°), and g = 9.8 m/s^2.
Solving for v gives v = √(2gh) = 3.64 m/s. So the correct answer is B.

Question 16

A hill is 150 m long and makes an angle of 12° with the horizontal.As a 60-kg jogger runs up the hill,how much work does gravity do on the jogger?
A)8.82E+4 J
B)1.83E+4 J
C)−1.83E+4 J
D)8.63E+4 J
E)zero

Accepted Answer

Gravity only acts vertically downwards, so it does no work on the jogger moving horizontally up the hill. The work done by gravity is given by the formula W = mgh, where m is the mass of the jogger, g is the acceleration due to gravity (9.81 m/s^2), and h is the height gained by the jogger. The height gained can be found by using trigonometry: 
h = 150 sin(12°) = 30.94 m
So the work done by gravity is W = (60 kg)(9.81 m/s^2)(30.94 m) = -1.83 x 10^4 J (negative because the work done by gravity is in the opposite direction to the displacement of the jogger). Therefore, the best answer choice is C.

Question 17

As an object is lowered into a deep hole in the surface of the Earth,which of the following must be assumed in regard to its potential energy?
A)increase
B)decrease
C)remain constant
D)cannot tell from the information given

Accepted Answer

As the object is lowered into a deep hole in the surface of the Earth, it moves closer to the center of the Earth, where the gravitational force is stronger. This results in a decrease in the object's gravitational potential energy because the object's distance from the Earth's surface decreases, which is the source of its potential energy.

Question 18

A 24.0-kg crate,initially at rest,slides down a ramp 4.0 m long and inclined at an angle of 20° with the horizontal.If there is no friction between ramp surface and crate,what is the kinetic energy of the crate at the bottom of the ramp? (g = 9.8 m/s²) A)880 J B)940 J C)644 J D)322 J E)161 J

Accepted Answer

The answer of A 24.0-kg crate,initially at rest,slides down a...

Question 19

A 2 500-kg car is moving at 2.30 m/s.How fast must a 1.5-kg toy car be moving so that the two have the same kinetic energy?
A)61.9 m/s
B)3.97 m/s
C)93.9 m/s
D)6 610 m/s

Accepted Answer

The answer of A 2 500-kg car is moving at...

Question 20

Two blocks are released from the top of a building.One falls straight down while the other slides down a smooth ramp.If all friction is ignored,which one is moving faster when it reaches the bottom?
A)The block that went straight down.
B)The block that went down the ramp.
C)They both will have the same speed.
D)Insufficient information to work the problem.

Accepted Answer

Both blocks will have the same speed. This is because the speed of the falling block depends only on the height from which it was dropped and not on the path it took. Similarly, the speed of the sliding block depends only on the vertical distance it traveled, which is the same as the height from which the other block was dropped. Therefore, both blocks will reach the bottom with the same speed.

Quiz 5: Energy

A 1 300-kg automobile moving at 21 m/s has the brakes applied with a deceleration of 3.0 m/s2.How far does the car travel before it stops?

What is the minimum amount of energy required for a 60.0-kg climber carrying a 18-kg pack to climb Mt.Everest,8 250 m high?

Which of the following is not true about potential energy?

A 8.00-kg bowling ball falls from a 3.50-m shelf.Just before hitting the floor,what will be its kinetic energy? (g = 9.80 m/s2 and assume air resistance is negligible)

A 1.00-kg ball has zero kinetic and potential energy.Ernie drops the ball into a 10.0-m-deep well.Just before the ball hits the bottom,the sum of its kinetic and potential energy is:

​Jasper takes two books of mass m1 and m2 off the floor and places them on a shelf at height h.The change in potential energy of the book with mass m1 is four times that of the book with mass m2.What is the relationship between m1 and m2?

A professional skier reaches a speed of 58.0 m/s on a 30° ski slope.Ignoring friction,what was the minimum distance along the slope the skier would have had to travel,starting from rest?

A horizontal force of 200 N is applied to a 55.0-kg cart across a 15.0-m level surface.If the cart accelerates at 2.0 m/s2,then what is the work done by the force of friction as it acts to retard the motion of the cart?

A boat with mass 950 kg is heading into the harbor at a speed of 10.0 m/s.How much work is required to slow the boat to 1.0 m/s?

A rock is thrown straight up with an initial velocity of 15.0 m/s.Ignore energy lost to air friction.How high will the rock rise?

A boat with mass of 1 200 kg is traveling at 12 m/s.What is the magnitude of the force required to stop the boat if it undergoes a displacement of 85 m?

Samantha pushes a 60-N crate up a ramp 30 m in length and inclined at 10° with the horizontal.What potential energy change does the crate experience?

A golf ball hits a wall and bounces back at 3/4 the original speed.What part of the original kinetic energy of the ball did it lose in the collision?

A 6.1-g bullet has a velocity of 475 m/s when it penetrates a wooden door to a depth of 3.5 cm.Assuming the frictional force that stops the bullet is constant,how long does it take from the time the bullet hits the door till it comes to a stop?

A 10.0-kg box starts at rest and slides 3.90 m down a ramp inclined at an angle of 10° with the horizontal.If there is no friction between the ramp surface and crate,what is the velocity of the crate at the bottom of the ramp? (g = 9.8 m/s2)

A hill is 150 m long and makes an angle of 12° with the horizontal.As a 60-kg jogger runs up the hill,how much work does gravity do on the jogger?

As an object is lowered into a deep hole in the surface of the Earth,which of the following must be assumed in regard to its potential energy?

A 24.0-kg crate,initially at rest,slides down a ramp 4.0 m long and inclined at an angle of 20° with the horizontal.If there is no friction between ramp surface and crate,what is the kinetic energy of the crate at the bottom of the ramp? (g = 9.8 m/s2)

A 2 500-kg car is moving at 2.30 m/s.How fast must a 1.5-kg toy car be moving so that the two have the same kinetic energy?

Two blocks are released from the top of a building.One falls straight down while the other slides down a smooth ramp.If all friction is ignored,which one is moving faster when it reaches the bottom?

A 1 300-kg automobile moving at 21 m/s has the brakes applied with a deceleration of 3.0 m/s².How far does the car travel before it stops?

A 8.00-kg bowling ball falls from a 3.50-m shelf.Just before hitting the floor,what will be its kinetic energy? (g = 9.80 m/s² and assume air resistance is negligible)

Jasper takes two books of mass m₁ and m₂ off the floor and places them on a shelf at height h.The change in potential energy of the book with mass m₁ is four times that of the book with mass m₂.What is the relationship between m₁ and m₂?

A horizontal force of 200 N is applied to a 55.0-kg cart across a 15.0-m level surface.If the cart accelerates at 2.0 m/s²,then what is the work done by the force of friction as it acts to retard the motion of the cart?

A 10.0-kg box starts at rest and slides 3.90 m down a ramp inclined at an angle of 10° with the horizontal.If there is no friction between the ramp surface and crate,what is the velocity of the crate at the bottom of the ramp? (g = 9.8 m/s²)

A 24.0-kg crate,initially at rest,slides down a ramp 4.0 m long and inclined at an angle of 20° with the horizontal.If there is no friction between ramp surface and crate,what is the kinetic energy of the crate at the bottom of the ramp? (g = 9.8 m/s²)