Physics Ch 6

When doing energy problems, which of the following can be replaced with ΔU?

- Wcons

For a conservative force, if WA→B = +20 J, then what is WB→A?

-20 J

The force acting on an object and the object's displacement are in opposite directions. Select all of the following that are possible values for the work done on the object.

-20 J -60 J

Which of the following is equal to the force exerted by an ideal spring?

-kx

A 1 kg mass is attached to a vertical spring, stretching it by 10 cm from its equilibrium position. With the spring secured in the same stretched position, the 1 kg mass is removed and replaced with a 0.50 kg mass. If the spring is then released, how high will the 0.50 kg mass rise above the point where it was released?

.10 m

A 1.80-kg block is released from rest and allowed to slide down a frictionless surface and into a spring. The far end of the spring is attached to a wall, as shown. The initial height of the block is 0.500 m above the lowest part of the slide and the spring constant is 463 N/m. What is the maximum compression of the spring?

.1952 m

A shooting star is a meteoroid that burns up when it reaches Earth's atmosphere. Many of these meteoroids are quite small. Compare the kinetic energy of a shooting star to that of a moving car. What is the kinetic energy of a 1009-kg car moving at 29.2 m/s (65.3 mi/h)?

.4301568 MJ

A 1.80-kg block is released from rest and allowed to slide down a frictionless surface and into a spring. The far end of the spring is attached to a wall, as shown. The initial height of the block is 0.500 m above the lowest part of the slide and the spring constant is 463 N/m. The spring sends the block back to the left. How high does the block rise?

.500 m

Rank from the smallest at top to the largest at the bottom the work done by a spring resulting from stretching or compressing the spring the specified distance. Assume that the spring constant is constant and that the spring is initially neither stretched nor compressed.

0 -2 6 -8

The force of magnitude 10 N acting on an object and the object's displacement of magnitude 3 m are perpendicular. What is the work done on the object by the force?

0 J

Select all of the following that are possible values for kinetic energy.

0 J 30 J

Rank the magnitude of the force exerted by the four springs below based on the given spring constants and displacements from equilibrium, with the largest magnitude at the top and the smallest at the bottom.

0.3m, 30N/m 0.6 10 -0.5 10 0, 400

For the four displacements listed below, rank the magnitude of the associated spring force, with the largest magnitude at the top and the smallest magnitude at the bottom. Assume all springs have the same spring constant.

0.6 -0.5 0.3 0

The tension in a ligament in the human knee is approximately proportional to the extension of the ligament, if the extension is not too large. If a particular ligament has an effective spring constant of 155 N/mm as it is stretched, what is the tension in this ligament when it is stretched by 0.710 cm?

1.1 kN

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

1.4 × 1014 kg

What is the minimum speed with which a meteor strikes the top of Earth's stratosphere (about 41.5 km above the surface), assuming that the meteor begins as a bit of interplanetary debris far from Earth and stationary relative to Earth? Assume that the drag force is negligible until the meteor reaches the stratosphere. Mass of Earth is 5.974 × 1024 kg; radius of Earth is 6.371 × 106 m; and gravitational constant is 6.674 × 10−11 N·m2/kg2.

11.148 km/s

An object of mass m moves with speed 3v. If the speed is doubled, then what will be the kinetic energy?

18mv2

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 friction and air resistance to be negligible, and treating kinetic energy as purely translational (i.e., ignoring any rotational part), what is his final speed?

198 km/h

A spring is used to propel a toy car across the floor. If you wish to double the launch speed of the toy car, by what factor must you change the distance the spring is initially compressed?

2

A spring with spring constant k = 2000 N/m is compressed by 0.02 m. After the spring is released, with what initial speed does the spring horizontally propel an object of mass 0.2 kg?

2 m/s

An ideal spring has a spring constant k = 22.9 N/m. What is the amount of work that must be done to stretch the spring 0.440 m from its relaxed length?

2.21672 J

A dragster drives a quarter mile (402 m) at a constant rate of acceleration, starting from rest and finishing the race with a final speed of 450 km/hr. The mass of the dragster, together with its driver, is 975 kg. What average power is provided by the engine, if 50% of the power output is delivered to the wheels? Neglect dissipative forces.

2.4 MW

A spring-powered dart gun is unstretched and has a spring constant 150 N/m. The spring is compressed by 8.00 cm and a 5.00 gram projectile is placed in the gun. The maximum height of the projectile when it is shot at an angle of 30.0 degrees above the horizontal from the gun is

2.45 m

An arrangement of two pulleys, as shown in the figure, is used to lift a 70.6-kg crate a distance of 4.24 m above the starting point. Assume the pulleys and rope are ideal and that all rope sections are essentially vertical. How much work must be done to lift the crate a distance of 4.24 m?

2.93357 kJ

An arrangement of two pulleys, as shown in the figure, is used to lift a 70.6-kg crate a distance of 4.24 m above the starting point. Assume the pulleys and rope are ideal and that all rope sections are essentially vertical. What is the change in the potential energy of the crate when it is lifted a distance of 4.24 m?

2.93357 kJ

If the work done by gravity from point A to point B is equal to 20 J, then how much work would be done by gravity from point A to point B along a longer, less steep route?

20 J

The force acting on an object and the object's displacement are in the same direction. Select all of the following that are possible values for the work done on the object.

20 J 60 J

The explosion in a cannon exerts an average force of 30,000 N for 2.00 meters. The velocity of a 2.00 kg projectile shot from the cannon is

245 m/s

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

2Mg(h+d)/d2

Rank the escape speed for a planet of radius 2 x 106 m, given the possible planet masses listed below. List in order of decreasing escape speed with the largest escape speed listed at the top and the smallest at the bottom.

2x10^11 1x10^10 5x10^9

When the escape speed from the surface of a spherical object of mass M and radius R is equal to the speed of light, that radius is called the Schwarzschild radius for the given mass. What is the Schwarzschild radius of the Sun, whose mass is 2.0 × 1030 kg? (i.e., if all the Sun's mass were compressed into a sphere of this radius, the escape speed from its surface would be the speed of light—it would become a black hole!)

3.0 km

If the speed of an object increases from v to 2v, then how much total work is done?

3/2 mv^2

A spring-powered launcher has a spring with a constant of 50.0 N/cm. The launcher is prepared by compressing the spring by 5.00 cm. If the mass of the projectile is 10.0 grams, what is the speed of the projectile when it is launched?

35.4 m/s

A 75.0 kg skier, starting from rest, slides down a 75.0 m high slope without friction. The velocity of the skier at the bottom of the slope is

38.3 m/s

A 200 N box is pushed at a constant velocity up an incline that is 5.00 m long and rises 1.00 m. The incline has a coefficient of kinetic friction of 0.200, and the pushing force is parallel to the incline. The work done by the pushing force is

396 J

A box slides down a 6.00 m long incline. The incline is 20.0° above the horizontal. The box is released from rest. The coefficient of friction between the box and the incline is 0.200. What is its speed at the bottom of the incline?

4.25 m/s

The equation for a particular force as a function of position is Fx(x) = (5 N/m)x. How much work does this force do on a particle that moves from x = 0 m to x = 4 m?

40 J

A 6.00 kg box is pulled up an 8.00 m long incline (with friction) at an angle of 30.0 degrees by a force of 50.0 N parallel to the incline. The coefficient of kinetic friction is 0.100. The work done against friction is

40.7 J

A crate of mass m1 = 12.4 kg is pulled by a massless rope up a 36.9° ramp. The rope passes over an ideal pulley and is attached to a hanging crate of mass m2 = 16.3 kg. The crates move 1.40 m, starting from rest. If the frictional force on the sliding crate has magnitude 19.4 N and the tension in the rope is 121.5 N, find the total work done on the sliding crate. The total work done on the sliding crate is

40.79 J

The graph shows the force on an object as it moves a distance x. What is the work done by the force as the object moves from 2.0 m to 8.0 m?

48 J

A 1.0 kg ball is launched into the air with an initial speed of 14 m/s at an unknown angle and follows a parabolic path. What is the kinetic energy of the ball at 5.0 m above its launching point if it is on its way down after passing through the peak of its motion?

49 J

An 8000 kg satellite is launched from the surface of the Earth into outer space. What initial kinetic energy is needed by the satellite in order to reach a great (i.e., infinite) distance from the Earth, neglecting the effects of air resistance in the atmosphere? (G = 6.67 × 10−11 N·m2/kg2, ME = 5.97 × 1024 kg, RE = 6.37 × 106 m.)

5.00 × 1011 J.

A 2.00 kg pendulum bob on a string 2.00 m long, is released with a velocity of 1.50 m/s when the support string makes an angle of 30.0 degrees with the vertical. What is the tangential acceleration of the bob at the highest point of its motion?

5.77 m/s^2

A shooting star is a meteoroid that burns up when it reaches Earth's atmosphere. Many of these meteoroids are quite small. Compare the kinetic energy of a shooting star to that of a moving car. What is the kinetic energy of a meteoroid of mass 5.10 g moving at a speed of 47.8 km/s?

5.82634 MJ

The equation for a particular force as a function of position is Fx(x) = (4 N/m)x. How much work does this force do on a particle that moves from x = 0 m to x = 5 m?

50 J

During a basketball game, a player shoots a ball from half-court. When the ball reaches its maximum height of 4.5 m above the floor, it is moving at 5.0 m/s. If the ball was released from 2.5 m above the floor, what was the angle above the horizontal of the ball's initial velocity?

51 degrees

A 20.0 kg box slides down a 12.0 m long incline at an angle of 30.0 degrees with the horizontal. A force of 50.0 N is applied to the box in the upward direction. The applied force F makes an angle of 0.00 to the incline. If the incline is frictionless, then the increase in the kinetic energy of the box is

576 J

The graph shows the force on an object as it moves a distance x. What is the work done by the force as the object moves from 0.0 m to 10.0 m?

64 J

A motorist driving a 1373-kg car on level ground accelerates from 20.0 m/s to 30.0 m/s in a time of 5.00 s. Ignoring friction and air resistance, determine the average mechanical power in watts the engine must supply during this time interval.

68.65 kW

A 2.00 kg pendulum bob on a string 1.50 m long, is released with a velocity of 4.00 m/s when the support string makes an angle of 30.0 degrees with the vertical. What is the angle with the vertical the bob makes at the highest point of its motion?

71.2 degrees

A planet with a radius of 6.00 × 107 m has a gravitational field of magnitude 49.8 m/s2 at the surface. What is the escape speed from the planet?

77.340459 km/s

An arrangement of two pulleys, as shown in the figure, is used to lift a 70.6-kg crate a distance of 4.24 m above the starting point. Assume the pulleys and rope are ideal and that all rope sections are essentially vertical. What length of rope must be pulled to lift the crate 4.24 m?

8.48 m

A car with mass of 1077 kg accelerates from 0 m/s to 40.0 m/s in 10.0 s. Ignore air resistance. The engine has a 22.0% efficiency, which means that 22.0% of the energy released by the burning gasoline is converted into mechanical energy. What is the average mechanical power output of the engine?

86.16 kW

An object that weighs 10 N is moved down and to the right along the entire length of a straight line. The line is 10 m long and makes a 60-degree angle with the horizontal. How much work does the gravitational force do on the object?

87 J

Select all of the following that always occur when work is done.

A force acts. An object moves. Energy is transferred.

Rank the change in gravitational potential energy with the largest change in gravitational potential energy at the top and the smallest at the bottom. The mass of the object is the same in each case.

An object moves from the sea level to the top of a large mountain An object moves from sea level to 5m above sea level An object moves horizontally

A book slows down as it slides across a floor that is horizontal, neither tilted up nor down. Select all of the following statements that are true.

Both the temperature of the book and the temperature of the floor increase. Friction converts kinetic energy into internal energy.

For an ideal spring, select all of the following that would result in a spring force magnitude equal to kx.

Compressing a spring with spring constant k a distance x from equilibrium Stretching a spring with spring constant k a distance x from equilibrium

Select all of the following forces that have a corresponding potential energy.

Conservative force Gravitational force Elastic force Electric force

Rank the following according to the average power, with the largest average power at the top and the smallest at the bottom.

Energy transferred = 100 J, elapsed time = 10s Energy transferred = 100 J, elapsed time = 20s Energy transferred = 200 J, elapsed time = 50s

A block is held some distance above a vertically oriented, relaxed spring. Which quantities are needed to determine the lowest point the block reaches after it is released?

Final elastic potential energy Initial elastic potential energy Final gravitational potential energy Initial gravitational potential energy

Rank the following according to the instantaneous power, with the largest instantaneous power at the top and the smallest at the bottom.

Force= (10 N, north), velocity = (10m/s, north) Force= (20 N, north), velocity = (20m/a, east) Force= (30 N, north), Velocity = (30m/s, south)

Which of the following corresponds to the equation Fx = -kx?

Hooke's law

A ball is thrown off the top of a building and lands on the ground below. Which quantities are needed to determine the kinetic energy of the ball just before it hits the ground?

Initial gravitational potential energy Initial kinetic energy Final gravitational potential energy

Rank the following according to the mechanical energy with the largest mechanical energy at the top and the smallest at the bottom.

K= 100J, U= 100J K= 0J, U= 100J K= 0J, U= 0J K= 0J, U= -100J

Rank the total work with the largest at the top and the smallest at the bottom.

Kf =30J, Ki= 0J Kf= 30J, Ki= 10J Kf= 30 J, Ki= 40J

What are the SI units for spring constant?

N/m

Select all of the following units that are equivalent to joules.

N⋅m kg⋅m2/s2

An object of mass 10 kg moves in one direction at 10 m/s along one straight line for 10 seconds. What is the total work done on the object?

O J

Choose the correct equation for instantaneous power. Theta is the angle between the force and velocity, and the angle between the force and displacement.

P = Fv cosΘ

Identify the statement that is true of potential energy.

Potential energy depends on position.

In Hooke's law, what does the symbol k mean?

Spring constant

Select all of the following that are needed to determine the total work done on an object.

The magnitude of the displacement The direction of the displacement The direction of the net force The magnitude of the net force

A shooting star is a meteoroid that burns up when it reaches Earth's atmosphere. Many of these meteoroids are quite small. Compare the kinetic energy of a shooting star to that of a moving car. What comparison can be drawn between the kinetic energy of the meteoroid and that of the car?

The meteoroid has more than 14 times the kinetic energy of the car.

An ideal rope-and-pulley system is used to lift a pallet of bricks. The advantage of an ideal rope-and-pulley system is that less force is required to lift the object than if it were lifted without mechanical aid. Which statement is correct?

The total work done is the same as it would be if the mechanical aid were not used.

A mass attached to a spring is displaced from equilibrium. Which statement is always true?

The work done by the spring force is negative.

According to equation 6-27, for two spherical objects, the gravitational potential energy depends on which of the following?

Their masses The distance between their centers

Compare the escape speed of Planet E to Planet X: the mass and radius of Planet E is twice that of Planet X.

They are the same

Which quantities are identified by conservation laws?

Those that do not change with time

What are the symbol and SI units for potential energy?

U, joules

Select all of the following that are SI units of power.

W kg m^2/s^3 J/s

Identify the correct equation for the total work done on an object.

Wtotal = Wcons + Wnc

Select all of the following that are equivalent to the work-kinetic energy theorem.

Wtotal = ΔK Wtotal = 1212mvf2 - 1212mvi2

When we say that a quantity does not change during any physical process, we call that a ______ law

conservation

All potential energies have a ______ force associated with them.

conservative

If mechanical energy is conserved and the potential energy increases, then what happens to the kinetic energy?

decreases

The conversion of energy into a disorganized form is called ______

dissipation

Select all of the following quantities that are included in the definition of average power.

energy transferred elapsed time

True or false: Conservative forces can change mechanical energy.

false

Select all of the following that are forms of macroscopic mechanical energy.

kinetic and potential

Rank the work done by the gravitational force with the largest work done at the top and the smallest at the bottom.

lowered 10m 10N is stationary is raised 5m raised 10m

What are the possible values of gravitational potential energy given by equation 6-27?

negative approx. zero

Select all of the following that are fundamental forms of energy.

rest potential kinetic

Is kinetic energy a vector or a scalar?

scalar

Work is a _______ quantity; it does not have a direction, but it can be positive, negative, or zero.

scalar

How much work is done by the gravitational force when an object moves horizontally?

zero

You are pulling your kid brother in a wagon at a constant speed. What is the total work done on the wagon?

zero

A ball is thrown straight up. What is its kinetic energy when it reaches its highest point? Select all that apply.

zero smallest possible

Select all of the following that correspond to the law of conservation of mechanical energy. The subscripts are f for final and i for initial.

ΔK + ΔU = 0 Kf + Uf = Ki + Ui

An 8000 kg satellite is launched from the surface of the Earth and injected into a circular orbit at an altitude of 100 km above the surface of the Earth. The gravitational potential energy of the satellite in the circular orbit is (G = 6.67 × 10−11 N·m2/kg2, ME = 5.97 × 1024 kg, RE = 6.37 × 106 m)

−4.92 × 1011 J.