Question 1

An airplane has a mass of 30,000 kg and travels at 300 m/s.If the drag force is 1000 N,the power the engines have to provide to keep flying at a constant speed is A) 6.0 $\times$ 10⁵ W B) 5.5 $\times$ 10⁵ W C) 4.9 $\times$ 10⁵ W D) 4.2 $\times$ 10⁵ W E) 3.0 $\times$ 10⁵ W

Accepted Answer

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Question 2

An asteroid,of radius 2.1 km,is observed to have an escape speed equal to a typical person's speed attained by jumping off , 3.0 m/s.What is its mass? A) 4.2 $\times$ 10¹⁴ kg B) 2.8 $\times$ 10¹⁴ kg C) 5.7 $\times$ 10¹⁴ kg D) 0.5 $\times$ 10¹⁴ kg E) 1.4 $\times$ 10¹⁴ kg

Accepted Answer

The answer of An asteroid,of radius 2.1 km,is observed to...

Question 3

A student lifts a weight of 10.0 N a distance of 0.5 meters.If this exercise is repeated 50 times in 100 seconds,then the power of this exercise is
A) 2.5 Watts.
B) 3.1 Watts.
C) 3.6 Watts.
D) 4.0 Watts.
E) 4.8 Watts.

Accepted Answer

The work done in one lift is 10.0 N * 0.5 m = 5.0 J. Repeating this 50 times results in 250 J. Power is work done over time, so 250 J / 100 s = 2.5 Watts.

Question 4

A 2500 kg car accelerates from rest to a velocity of 10 m/s in 5.0 seconds.The power of the engine during this acceleration is
A) 50 kW.
B) 47 kW.
C) 40 kW.
D) 31 kW.
E) 25 kW.

Accepted Answer

The answer of A 2500 kg car accelerates from rest...

Question 5

A car has a mass of 2,000 kg and travels at 20.0 m/s.If the drag force is 100 N,the power the engines have to provide to keep moving at constant speed is
A) 2.0 kW.
B) 2.9 kW.
C) 3.4 kW.
D) 3.9 kW.
E) 4.2 kW.

Accepted Answer

The power required to overcome the drag force is calculated using the formula Power = Force x Velocity. Here, Power = 100 N x 20.0 m/s = 2000 W, which is 2.0 kW.

Question 6

A comet is observed to pass 1.50 $\times$ 10⁸ m from the surface of the sun.The sun's radius is 6.96 $\times$ 10⁸ m.What is the speed of the comet at this point,if its speed when passing the Earth's orbit,1.50 $\times$ 10¹¹ m from the sun's center,is 25km/s? A) 561 km/s B) 618 km/s C) 562 km/s D) 585 km/s

Accepted Answer

Using the conservation of energy, the speed of the comet can be calculated. The gravitational potential energy and kinetic energy at both points are equated, leading to the speed of approximately 561 km/s at the closest approach to the sun.

Question 7

A blob of clay,mass M,is propelled upward from a spring that is initially compressed by an amount d.If,upon its release,the clay reaches an ultimate height of h above the unstretched spring's end,what is the spring constant k? A) kd²/(mg) B) kd²/(2mg)- d C) kd²/(mg)-d D) kd²/(2mg)

Accepted Answer

The answer of A blob of clay,mass M,is propelled upward...

Question 8

A 1800 kg car moving at 20 m/s hits an initially uncompressed spring with a spring constant of 2.0 $\times$ 10⁶ N/m.The maximum compression of the spring is A) 0.40 m. B) 0.60 m. C) 0.80 m. D) 1.0 m. E) 1.2 m.

Accepted Answer

The maximum compression of the spring can be found using energy conservation: the initial kinetic energy of the car is converted into the potential energy of the spring. Using the formula (1/2)mv^2 = (1/2)kx^2, where m = 1800 kg, v = 20 m/s, and k = 2.0 * 10^6 N/m, solving for x gives 0.60 m.

Question 9

A 1.1 kg seagull takes off from a piling along the California coast and accelerates within 0.50s to a flight speed of 7.5m/s along a horizontal path.What average power was developed by the bird's wings as it accelerated?
A) 62W
B) 8.3W
C) 33W
D) 250W

Accepted Answer

The average power is the work done per unit time. The work done by the bird's wings is equal to the change in kinetic energy of the bird. The change in kinetic energy is:$$\Delta K = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2$$where:* $m$ is the mass of the bird* $v_f$ is the final velocity of the bird* $v_i$ is the initial velocity of the birdThe average power is then:$$P = \frac{\Delta K}{\Delta t} = \frac{\frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2}{\Delta t}$$Substituting the given values, we get:$$P = \frac{\frac{1}{2}(1.1	ext{ kg})(7.5	ext{ m/s})^2 - 0}{(0.50	ext{ s})}$$$$P = 62	ext{ W}$$

Question 10

An asteroid,of mass 1.4 $\times$ 10¹⁴ kg is observed to have an escape speed equal to a typical person's speed attained by jumping off,3.0m/s.What is its radius? A) 6.3 km B) 2.1 km C) 1.0 km D) 0.5 km

Accepted Answer

The answer of An asteroid,of mass 1.4 $\times$ 10¹⁴ kg...

Question 11

A ski lift carries passengers up a 150 m high slope at the rate of one chair every 30.0 seconds.If the chair will hold two passengers with a total mass of 190 kg,then the power of the engine that powers the ski lift is
A) 6.96 kW.
B) 7.83 kW.
C) 8.75 kW.
D) 9.31 kW.
E) 9.90 kW.

Accepted Answer

First, we need to calculate the work done by the ski lift per chair:

Work = force x distance

The weight of the two passengers is:

m = 190 kg

The force required to lift them is:

F = mg = 190 kg x 9.8 m/s^2 = 1862 N

The distance lifted per chair is:

d = 150 m

Therefore, the work done per chair is:

W = F x d = 1862 N x 150 m = 279,300 J

The ski lift carries one chair every 30.0 seconds, so the power of the engine is:

P = W / t = 279,300 J / 30.0 s = 9310 W

We can then convert this to kW:

P = 9.31 kW

Therefore, the answer is D) 9.31 kW.

Question 12

A dragster drives a quarter mile (402 m)at a constant rate of acceleration,starting from rest and finishing the race at a final speed of 450 km/hr.If the mass of the dragster is 975 kg,together with its driver,and rolling friction is ignored,what average power was developed by the engine,if 50% of the power developed by the engine was delivered to the wheels?
A) 4.7 MW
B) 1.2 MW
C) 0.6 MW
D) 2.4 MW

Accepted Answer

The final speed is 450 km/hr, which is 125 m/s. Using the formula for kinetic energy (KE = 0.5 * m * v^2), the kinetic energy at the end is 0.5 * 975 kg * (125 m/s)^2. The work done is equal to this kinetic energy since it starts from rest. Power is work done over time, and time can be found using the formula v = at, where a is the acceleration. Solving for time and then power, considering only 50% of the engine power is delivered to the wheels, gives approximately 2.4 MW.

Question 13

A 2000 kg car accelerates from rest to a velocity of 20 m/s in 10 seconds.The power of the engine during this acceleration is
A) 50 kW.
B) 40 kW.
C) 30 kW.
D) 20 kW.
E) 10 kW.

Accepted Answer

We can use the formula for power:
Power = Work/Time
The work done on the car is equal to the change in kinetic energy (1/2mv^2) from rest to a velocity of 20 m/s:
Work = (1/2)(2000 kg)(20 m/s)^2 = 400,000 J
The time taken for the car to reach 20 m/s is given as 10 seconds.
Hence, Power = 400,000 J /10 s = 40,000 W = 40 kW.

Therefore, the correct answer is B) 40 kW.

Question 14

A blob of clay,mass M,is dropped onto a spring from a height h above the end of the spring.If the spring compresses an amount d as the blob comes to rest,what is the spring constant? A) 2mgh/d² B) mgh/d² C) mg(h+d)/d² D) 2mg(h+d)/d²

Accepted Answer

The potential energy from the height (mgh) and the additional potential energy from the spring compression (mgd) are converted into the spring's potential energy (1/2)kd^2. Solving for k gives k = 2mg(h+d)/d^2.

Question 15

During a basketball game,a player shoots a ball from half-court.When the ball reaches a height of 4.5 m above the floor,it is moving at 5.0 m/s.Assuming the shot was perfectly made,it will pass through the rim of the basket,3.05 m above the floor.How fast the ball moving when it passes through the rim?
A) 7.7 m/s
B) 7.3 m/s
C) 9.2 m/s
D) 5.3 m/s

Accepted Answer

The answer of During a basketball game,a player shoots a...

Question 16

A road bicycle racer rides down the highway from Pike's peak.During one stretch of the ride,he descends 150 m while accelerating from 35 km/hr to some final speed.Assuming rolling friction and air resistance to be negligible,what is that final speed?
A) 113 km/h
B) 118 km/h
C) 148 km/h
D) 169 km/h

Accepted Answer

The answer of A road bicycle racer rides down the...

Question 17

A spring-powered dart gun is un-stretched and has a spring constant 10.0 N/m.The spring is compressed by 8.00 cm and a 5.00 gram projectile is placed in the gun.The kinetic energy of the projectile when it is shot from the gun is
A) 0.020 J.
B) 0.032 J.
C) 0.060 J.
D) 0.100 J.
E) 0.120 J.

Accepted Answer

The kinetic energy of the projectile can be calculated using the formula for the potential energy stored in a compressed spring, which is given by $PE = \frac{1}{2}kx^2$, where $k$ is the spring constant and $x$ is the compression distance. Here, $k = 10.0 \, \text{N/m}$ and $x = 8.00 \, \text{cm} = 0.080 \, \text{m}$. Plugging these values into the formula gives $PE = \frac{1}{2} \times 10.0 \, \text{N/m} \times (0.080 \, \text{m})^2 = 0.032 \, \text{J}$. This potential energy is converted into kinetic energy as the projectile is shot from the gun, so the kinetic energy of the projectile is 0.032 J.

Question 18

A 90.0 kg person is running up the stairs at 0.500 m/s.The power needed to run up the stairs is
A) 441 Watts.
B) 395 Watts.
C) 302 Watts.
D) 275 Watts.
E) 257 Watts.

Accepted Answer

The power needed is calculated using the formula P = mgh/t, where m is mass, g is gravity, h is height, and t is time. Since velocity v = h/t, we can use P = mgv. Substituting m = 90.0 kg, g = 9.8 m/s², and v = 0.500 m/s, we get P = 90.0 * 9.8 * 0.500 = 441 Watts.

Question 19

A 1.1 kg seagull takes off from a piling along the California coast and accelerates within 0.50 s to a flight speed of 7.5 m/s along a slightly inclined path.At the end of the 0.50 s period,it is 5.3 m above its point of takeoff.What power was developed by the bird's wings?
A) 180 W
B) 110 W
C) 52 W
D) 62 W

Accepted Answer

The power developed by the bird's wings is equal to the rate at which it does work. The work done by the bird is equal to the change in its kinetic energy plus the change in its potential energy. The change in kinetic energy is:$$\Delta K = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2$$where m is the mass of the bird, $v_i$ is its initial velocity, and $v_f$ is its final velocity. The change in potential energy is:$$\Delta U = mgh$$where g is the acceleration due to gravity and h is the height to which the bird has risen. The power developed by the bird's wings is:$$P = \frac{\Delta K + \Delta U}{\Delta t}$$where $\Delta t$ is the time interval over which the work is done. Substituting the given values into this equation, we get:$$P = \frac{\frac{1}{2}(1.1 	ext{ kg})(7.5 	ext{ m/s})^2 + (1.1 	ext{ kg})(9.8 	ext{ m/s}^2)(5.3 	ext{ m})}{0.50 	ext{ s}} = 180 	ext{ W}$$Therefore, the correct answer is A.

Question 20

If the escape speed of a star is equal to the speed of light,its radius is the so-called Schwarzschild radius.What is the Schwarzschild radius of the sun,whose mass is 2.0 $\times$ 10³⁰ kg? A) 4.5 km B) 1.5 km C) 5.9 km D) 3.0 km

Accepted Answer

The Schwarzschild radius (R_s) is calculated using the formula R_s = 2GM/c^2. For the sun, with G = 6.674 x 10^-11 m^3 kg^-1 s^-2, M = 2.0 x 10^30 kg, and c = 3.0 x 10^8 m/s, R_s ≈ 3.0 km.

Quiz 6: Conservation of Energy

An airplane has a mass of 30,000 kg and travels at 300 m/s.If the drag force is 1000 N,the power the engines have to provide to keep flying at a constant speed is

An asteroid,of radius 2.1 km,is observed to have an escape speed equal to a typical person's speed attained by jumping off , 3.0 m/s.What is its mass?

A student lifts a weight of 10.0 N a distance of 0.5 meters.If this exercise is repeated 50 times in 100 seconds,then the power of this exercise is

A 2500 kg car accelerates from rest to a velocity of 10 m/s in 5.0 seconds.The power of the engine during this acceleration is

A car has a mass of 2,000 kg and travels at 20.0 m/s.If the drag force is 100 N,the power the engines have to provide to keep moving at constant speed is

A comet is observed to pass 1.50 ×\times× 108 m from the surface of the sun.The sun's radius is 6.96 ×\times× 108 m.What is the speed of the comet at this point,if its speed when passing the Earth's orbit,1.50 ×\times× 1011 m from the sun's center,is 25km/s?

A blob of clay,mass M,is propelled upward from a spring that is initially compressed by an amount d.If,upon its release,the clay reaches an ultimate height of h above the unstretched spring's end,what is the spring constant k?

A 1800 kg car moving at 20 m/s hits an initially uncompressed spring with a spring constant of 2.0 ×\times× 106 N/m.The maximum compression of the spring is

A 1.1 kg seagull takes off from a piling along the California coast and accelerates within 0.50s to a flight speed of 7.5m/s along a horizontal path.What average power was developed by the bird's wings as it accelerated?

An asteroid,of mass 1.4 ×\times× 1014 kg is observed to have an escape speed equal to a typical person's speed attained by jumping off,3.0m/s.What is its radius?

A ski lift carries passengers up a 150 m high slope at the rate of one chair every 30.0 seconds.If the chair will hold two passengers with a total mass of 190 kg,then the power of the engine that powers the ski lift is

A 2000 kg car accelerates from rest to a velocity of 20 m/s in 10 seconds.The power of the engine during this acceleration is

A blob of clay,mass M,is dropped onto a spring from a height h above the end of the spring.If the spring compresses an amount d as the blob comes to rest,what is the spring constant?

A road bicycle racer rides down the highway from Pike's peak.During one stretch of the ride,he descends 150 m while accelerating from 35 km/hr to some final speed.Assuming rolling friction and air resistance to be negligible,what is that final speed?

A spring-powered dart gun is un-stretched and has a spring constant 10.0 N/m.The spring is compressed by 8.00 cm and a 5.00 gram projectile is placed in the gun.The kinetic energy of the projectile when it is shot from the gun is

A 90.0 kg person is running up the stairs at 0.500 m/s.The power needed to run up the stairs is

A 1.1 kg seagull takes off from a piling along the California coast and accelerates within 0.50 s to a flight speed of 7.5 m/s along a slightly inclined path.At the end of the 0.50 s period,it is 5.3 m above its point of takeoff.What power was developed by the bird's wings?

If the escape speed of a star is equal to the speed of light,its radius is the so-called Schwarzschild radius.What is the Schwarzschild radius of the sun,whose mass is 2.0 ×\times× 1030 kg?

A comet is observed to pass 1.50 $\times$ 10⁸ m from the surface of the sun.The sun's radius is 6.96 $\times$ 10⁸ m.What is the speed of the comet at this point,if its speed when passing the Earth's orbit,1.50 $\times$ 10¹¹ m from the sun's center,is 25km/s?

A 1800 kg car moving at 20 m/s hits an initially uncompressed spring with a spring constant of 2.0 $\times$ 10⁶ N/m.The maximum compression of the spring is

An asteroid,of mass 1.4 $\times$ 10¹⁴ kg is observed to have an escape speed equal to a typical person's speed attained by jumping off,3.0m/s.What is its radius?

If the escape speed of a star is equal to the speed of light,its radius is the so-called Schwarzschild radius.What is the Schwarzschild radius of the sun,whose mass is 2.0 $\times$ 10³⁰ kg?