Question 1

An all-terrain vehicle of 2 000 kg mass moves up a 15.0$\degree$ slope at a constant velocity of 6.00 m/s.The rate of change of gravitational potential energy with time is

Accepted Answer

A) 5.25 kW. 
B) 24.8 kW. 
C) 30.4 kW. 
D) 118 kW. 
E) 439 kW. 
A) 5.25 kW. 
B) 24.8 kW. 
C) 30.4 kW. 
D) 118 kW. 
E) 439 kW.

Question 2

A 0.80-kg object tied to the end of a 2.0-m string swings as a pendulum.At the lowest point of its swing,the object has a kinetic energy of 10 J.Determine the speed of the object at the instant when the string makes an angle of 50$\degree$with the vertical.

Accepted Answer

A) 5.6 m/s 
B) 4.4 m/s 
C) 3.3 m/s 
D) 5.0 m/s 
E) 6.1 m/s 
A) 5.6 m/s 
B) 4.4 m/s 
C) 3.3 m/s 
D) 5.0 m/s 
E) 6.1 m/s

Question 3

A pendulum is made by letting a 2.0-kg object swing at the end of a string that has a length of 1.5 m.The maximum angle the string makes with the vertical as the pendulum swings is 30$\degree$.What is the speed of the object at the lowest point in its trajectory?

Accepted Answer

A) 2.0 m/s 
B) 2.2 m/s 
C) 2.5 m/s 
D) 2.7 m/s 
E) 3.1 m/s 
A) 2.0 m/s 
B) 2.2 m/s 
C) 2.5 m/s 
D) 2.7 m/s 
E) 3.1 m/s

Question 4

A 1.6-kg block slides down a plane (inclined at 25$\degree$ with the horizontal)at a constant speed of 2.0 m/s.At what rate is the frictional force changing the mechanical energy of the block?

Accepted Answer

A) +28 W 
B) +13 W 
C) -13 W 
D) -28 W 
E) +6.5 W 
A) +28 W 
B) +13 W 
C) -13 W 
D) -28 W 
E) +6.5 W

Question 5

A block (mass = 4.0 kg)sliding on a horizontal frictionless surface is attached to one end of a horizontal spring (k = 100 N/m)which has its other end fixed.If the maximum distance the block slides from the equilibrium position is equal to 20 cm,what is the speed of the block at an instant when it is a distance of 16 cm from the equilibrium position?

Accepted Answer

A) 71 cm/s 
B) 60 cm/s 
C) 80 cm/s 
D) 87 cm/s 
E) 57 cm/s 
A) 71 cm/s 
B) 60 cm/s 
C) 80 cm/s 
D) 87 cm/s 
E) 57 cm/s

Question 6

A spring (k = 200 N/m)is suspended with its upper end supported from a ceiling.With the spring hanging in its equilibrium configuration,an object (mass = 2.0 kg)is attached to the lower end and released from rest.What is the speed of the object after it has fallen 4.0 cm?

Accepted Answer

A) 90 cm/s 
B) 79 cm/s 
C) 96 cm/s 
D) 83 cm/s 
E) 57 cm/s 
A) 90 cm/s 
B) 79 cm/s 
C) 96 cm/s 
D) 83 cm/s 
E) 57 cm/s

Question 7

A champion athlete can produce one horsepower (746 W)for a short period of time.If a 70-kg athlete were to bicycle to the summit of a 500-m high mountain while expending power at this rate,she would have used at least ____ J of energy.

Accepted Answer

A) 746 
B) 3.43 * 105 
C) 3.73 *105 
D) 7.46 * 105 
E) 2.61* 107 
A) 746 
B) 3.43 * 105 
C) 3.73 *105 
D) 7.46 * 105 
E) 2.61* 107

Question 8

The two masses in the figure are released from rest.After the 3.0-kg mass has fallen 1.5 m,it is moving with a speed of 3.8 m/s.What is the change in mechanical energy done on the system during this time interval by the frictional force on the 2.0 kg mass?

Accepted Answer

A) -12 J 
B) -17 J 
C) -20 J 
D) -8.0 J 
E) -28 J 
A) -12 J 
B) -17 J 
C) -20 J 
D) -8.0 J 
E) -28 J

Question 9

A spring (k = 600 N/m)is placed in a vertical position with its lower end supported by a horizontal surface.A 2.0-kg block that is initially 0.40 m above the upper end of the spring is dropped from rest onto the spring.What is the kinetic energy of the block at the instant it has fallen 0.50 m (compressing the spring 0.10 m)?

Accepted Answer

A) 5.3 J 
B) 6.8 J 
C) 6.3 J 
D) 5.8 J 
E) 6.5 J 
A) 5.3 J 
B) 6.8 J 
C) 6.3 J 
D) 5.8 J 
E) 6.5 J

Question 10

As a result of friction between internal parts of an isolated system

Accepted Answer

A) the total mechanical energy of the system increases. 
B) the total mechanical energy of the system decreases. 
C) the total mechanical energy of the system remains the same. 
D) the potential energy of the system increases but the kinetic energy remains the same. 
E) the kinetic energy of the system increases but the potential energy of the system remains the same. 
A) the total mechanical energy of the system increases. 
B) the total mechanical energy of the system decreases. 
C) the total mechanical energy of the system remains the same. 
D) the potential energy of the system increases but the kinetic energy remains the same. 
E) the kinetic energy of the system increases but the potential energy of the system remains the same.

Question 11

A spring (k = 600 N/m)is placed in a vertical position with its lower end supported by a horizontal surface.The upper end is depressed 20 cm,and a 4.0-kg block is placed on top of the depressed spring.The system is then released from rest.How far above the point of release will the block rise?

Accepted Answer

A) 46 cm 
B) 36 cm 
C) 41 cm 
D) 31 cm 
E) 20 cm 
A) 46 cm 
B) 36 cm 
C) 41 cm 
D) 31 cm 
E) 20 cm

Question 12

At what rate is the gravitational force on a 2.0-kg projectile doing work at an instant when the velocity of the projectile is 4.0 m/s directed 30$\degree$ above the horizontal?

Accepted Answer

A) +39 W 
B) -78 W 
C) -39 W 
D) +78 W 
E) +25 W 
A) +39 W 
B) -78 W 
C) -39 W 
D) +78 W 
E) +25 W

Question 13

Two masses,MA and MB,with MB = 2MA,are released at the same time and allowed to fall straight down.Neglect air resistance.When we compare their kinetic energies after they have fallen for equal times,we find that

Accepted Answer

A) KB = KA. 
B) KB = 2KA. 
C) KB = 4KA. 
D) KA = 2KB. 
E) KA = 4KB. 
A) KB = KA. 
B) KB = 2KA. 
C) KB = 4KA. 
D) KA = 2KB. 
E) KA = 4KB.

Question 14

A 25-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 12 J.What is the change in mechanical energy caused by the frictional force on the block as it moves the 2.0 cm?

Accepted Answer

A) -4.0 J 
B) -3.5 J 
C) -2.4 J 
D) -2.9 J 
E) -15 J 
A) -4.0 J 
B) -3.5 J 
C) -2.4 J 
D) -2.9 J 
E) -15 J

Question 15

The speed of a 4.0-kg object is given by v = (2t)m/s,where t is in s.At what rate is the resultant force on this object doing work at t = 1 s?

Accepted Answer

A) 48 W 
B) 40 W 
C) 32 W 
D) 56 W 
E) 16 W 
A) 48 W 
B) 40 W 
C) 32 W 
D) 56 W 
E) 16 W

Question 16

A 3.0-kg block is on a frictionless horizontal surface.The block is at rest when,at t = 0,a force (magnitude P = 2.0 N)acting at an angle of 22$\degree$ above the horizontal is applied to the block.At what rate is the force P doing work at t = 2.0 s?

Accepted Answer

A) 2.3 W 
B) 2.0 W 
C) 1.4 W 
D) 1.7 W 
E) 1.2 W 
A) 2.3 W 
B) 2.0 W 
C) 1.4 W 
D) 1.7 W 
E) 1.2 W

Question 17

A 2.0-kg block sliding on a horizontal frictionless surface is attached to one end of a horizontal spring (k = 200 N/m)which has its other end fixed.If the block has a speed of 4.0 m/s as it passes through the equilibrium position,what is its speed when it is 20 cm from the equilibrium position?

Accepted Answer

A) 2.6 m/s 
B) 3.1 m/s 
C) 3.5 m/s 
D) 1.9 m/s 
E) 2.3 m/s 
A) 2.6 m/s 
B) 3.1 m/s 
C) 3.5 m/s 
D) 1.9 m/s 
E) 2.3 m/s

Exam 7: Conservation of Energy

An all-terrain vehicle of 2 000 kg mass moves up a 15.0 °\degree° slope at a constant velocity of 6.00 m/s.The rate of change of gravitational potential energy with time is

A 0.80-kg object tied to the end of a 2.0-m string swings as a pendulum.At the lowest point of its swing,the object has a kinetic energy of 10 J.Determine the speed of the object at the instant when the string makes an angle of 50 °\degree° with the vertical.

A pendulum is made by letting a 2.0-kg object swing at the end of a string that has a length of 1.5 m.The maximum angle the string makes with the vertical as the pendulum swings is 30 °\degree° .What is the speed of the object at the lowest point in its trajectory?

A 1.6-kg block slides down a plane (inclined at 25 °\degree° with the horizontal)at a constant speed of 2.0 m/s.At what rate is the frictional force changing the mechanical energy of the block?

A spring (k = 200 N/m)is suspended with its upper end supported from a ceiling.With the spring hanging in its equilibrium configuration,an object (mass = 2.0 kg)is attached to the lower end and released from rest.What is the speed of the object after it has fallen 4.0 cm?

A champion athlete can produce one horsepower (746 W)for a short period of time.If a 70-kg athlete were to bicycle to the summit of a 500-m high mountain while expending power at this rate,she would have used at least ____ J of energy.

The two masses in the figure are released from rest.After the 3.0-kg mass has fallen 1.5 m,it is moving with a speed of 3.8 m/s.What is the change in mechanical energy done on the system during this time interval by the frictional force on the 2.0 kg mass?

As a result of friction between internal parts of an isolated system

A spring (k = 600 N/m)is placed in a vertical position with its lower end supported by a horizontal surface.The upper end is depressed 20 cm,and a 4.0-kg block is placed on top of the depressed spring.The system is then released from rest.How far above the point of release will the block rise?

At what rate is the gravitational force on a 2.0-kg projectile doing work at an instant when the velocity of the projectile is 4.0 m/s directed 30 °\degree° above the horizontal?

Two masses,MA and MB,with MB = 2MA,are released at the same time and allowed to fall straight down.Neglect air resistance.When we compare their kinetic energies after they have fallen for equal times,we find that

The speed of a 4.0-kg object is given by v = (2t)m/s,where t is in s.At what rate is the resultant force on this object doing work at t = 1 s?

A 3.0-kg block is on a frictionless horizontal surface.The block is at rest when,at t = 0,a force (magnitude P = 2.0 N)acting at an angle of 22 °\degree° above the horizontal is applied to the block.At what rate is the force P doing work at t = 2.0 s?

A 2.0-kg block sliding on a horizontal frictionless surface is attached to one end of a horizontal spring (k = 200 N/m)which has its other end fixed.If the block has a speed of 4.0 m/s as it passes through the equilibrium position,what is its speed when it is 20 cm from the equilibrium position?

Introduction and Vectors

Motion in One Dimension

Motion in Two Dimensions

The Laws of Motion

More Applications of Newtons Laws

Energy of a System

Momentum and Collisions

Relativity

Rotational Motion

Gravity,planetary Orbits,and the Hydrogen Atom

Oscillatory Motion

Mechanical Waves

Superposition and Standing Waves

Fluid Mechanics

Temperature and the Kinetic Theory of Gases

Energy in Thermal Processes: the First Law of Thermodynamics

Heat Engines,entropy,and the Second Law of Thermodynamics

Electric Forces and Electric Fields

Electric Potential and Capacitance

Current and Direct Current Circuits

Magnetic Forces and Magnetic Fields

Faradays Law and Inductance

Electromagnetic Waves

Reflection and Refraction of Light

Image Formation by Mirrors and Lenses

Wave Optics

Quantum Physics

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Filters

An all-terrain vehicle of 2 000 kg mass moves up a 15.0 $\degree$ slope at a constant velocity of 6.00 m/s.The rate of change of gravitational potential energy with time is

A 0.80-kg object tied to the end of a 2.0-m string swings as a pendulum.At the lowest point of its swing,the object has a kinetic energy of 10 J.Determine the speed of the object at the instant when the string makes an angle of 50 $\degree$ with the vertical.

A pendulum is made by letting a 2.0-kg object swing at the end of a string that has a length of 1.5 m.The maximum angle the string makes with the vertical as the pendulum swings is 30 $\degree$ .What is the speed of the object at the lowest point in its trajectory?

A 1.6-kg block slides down a plane (inclined at 25 $\degree$ with the horizontal)at a constant speed of 2.0 m/s.At what rate is the frictional force changing the mechanical energy of the block?

At what rate is the gravitational force on a 2.0-kg projectile doing work at an instant when the velocity of the projectile is 4.0 m/s directed 30 $\degree$ above the horizontal?

Two masses,M_A and M_B,with M_B = 2M_A,are released at the same time and allowed to fall straight down.Neglect air resistance.When we compare their kinetic energies after they have fallen for equal times,we find that

A 3.0-kg block is on a frictionless horizontal surface.The block is at rest when,at t = 0,a force (magnitude P = 2.0 N)acting at an angle of 22 $\degree$ above the horizontal is applied to the block.At what rate is the force P doing work at t = 2.0 s?