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Flashcards in Work & Energy Deck (42)
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1
Q

What is the work done by a force F which acts on an object as it moves through a distance d?

A

W = Fd cos(θ)

Here, θ is the angle between the force and the direction of motion.

Since work is proportional to cos(θ), only the component of force parallel to the motion contributes to the work; any forces perpendicular to the motion do no work since cos(90)=0.

2
Q

What are the units of work, as defined in physics?

A

Work has units of Joules (J).

Remember that work is defined as F * d cos(θ), which has units of N * m, or kg * m2/s2. These are identical to the units of Joules.

3
Q

What is the sign of work done on an object, if it begins at rest and an applied force accelerates it to a speed v?

A

The work done on the object by the force is positive (+).

By definition, work done by a force that leads to a change in distance, and hence an increase in speed, is positive work.

4
Q

What is the sign of work done on an object, if it begins at speed v and an applied force decelerates it to rest?

A

The work done on the object by the force is negative (-).

By definition, work done by a force (such as friction) that leads to a decrease in speed is negative work.

5
Q

What kind of work (positive or negative) can a person do by pushing on a box?

A

A person can do either positive or negative work by pushing on a box.

If the person pushes on the box in the same direction that it moves, accelerating it, then positive work is done. If the person pushes in the opposite direction of the moving box, decelerating it, then negative work is done.

6
Q

What kind of work (positive, negative, or both) can frictional forces do?

A

Frictional forces can only do negative work.

By definition, frictional forces are always in the opposite direction of an object’s motion. Hence, they can only slow the object down, and only do negative work.

7
Q

What expression gives the work done by gravity as an object of mass m moves from the ground to a height h?

A

W = mgh

Remember, W = F * d cos(θ). In this case, as an object moves straight up, θ = 0º and cos(θ) = 1. So, W = F * d. The force of gravity is simply mg, and the distance is h, so the total work done is mgh.

8
Q

An object at rest is moved from the ground to a height h/2, then to rest at a height h. How much work does gravity do during this process?

A

W = -mgh

The work done by gravity while the object moves to h/2 is -mg(h/2). The work done while the object is moving from h/2 to h is also -mg(h/2). Work is negative in this case, because gravity works against the object being moved.

Notice that this is identical to the work done if the object is moved directly to h; the work done by gravity is path-independent.

9
Q

Define:

mechanical advantage

A

Mechanical advantage is the multiplication of a force using a mechanical device. A small force exerted over a large distance is transformed into a larger force over a smaller distance.

On the MCAT, mechanical advantage appears primarily in problems including levers and pulleys.

10
Q

What is the relationship between force and distance in any system which includes mechanical advantage?

A

F1d1 = F2d2

In any system exhibiting mechanical advantage, the force exerted and the distance covered are inversely proportional. This occurs because work must be the same in both cases.

11
Q

A force F1 is exerted a distance d1 from the fulcrum of a lever. What does the force F2 at d2 from the other end equal?

A

F2 = F1d1 / d2

In any system exhibiting mechanical advantage, the force exerted and the distance are inversely proportional, F1d1 = F2d2. Rearranging yields the above relationship.

12
Q

A pulley system is set up that allows a weight m to be lifted using a force of only (1/3)mg. How far must the string on which the force is exerted be pulled in order to move the weight a distance of d?

A

The string must be pulled a distance of 3d.

In any system exhibiting mechanical advantage, the force exerted and the distance are inversely proportional, F1d1 = F2d2. If one-third of the force is required, the distance must increase by the same proportion.

13
Q

Define:

power

A

Power is a measure of the rate of energy flow.

Power is defined as energy divided by time:

P = E/t

The units of power are watts, where 1 W = 1 J/s.

14
Q

What is the power flowing through a wire. if 1,000 J of energy flow through in 0.1 s?

A

P = 10,000 W = 10 kW

Power is energy divided by time;

1000 / 0.1 = 10,000 W

Note that the kW is a commonly-used unit on the MCAT.

15
Q

Define:

the kinetic energy of an object

A

An object’s kinetic energy is the energy resulting from its motion.

Kinetic energy is defined as:

KE = ½mv2

where m is the object’s mass and v is its speed. The units of kinetic energy are Joules, just like the units of all other forms of energy.

16
Q

If Objects 1 and 2 are moving at the same speed, but Object 2 has twice the mass of Object 1, how do their kinetic energies compare?

A

KE2 = 2KE1

Kinetic energy is defined as ½mv2, so it is directly proportional to mass. If the objects’ speeds are the same, kinetic energy will increase proportionally with mass.

17
Q

If Objects 1 and 2 are the same mass, but Object 2 is moving at twice the speed of Object 1, how do their kinetic energies compare?

A

KE2 = 4KE1

Kinetic energy is defined as ½mv2, so it is directly proportional to the square of the velocity. If the objects’ masses are the same, kinetic energy will increase with velocity squared.

18
Q

Define:

work-energy theorem

A

The work-energy theorem states that the net work done on an object by all the forces acting on it equals the change in the object’s kinetic energy.

Wnet = ΔKE

19
Q

An object is initially at rest. A person then pushes on it, doing 50 J of work that convert to motion. What is the object’s final kinetic energy?

Assume no dissipative forces are present.

A

The object’s final KE is 50 J.

According to the work-energy theorem, the net work done on the object results in a change in its kinetic energy. Since the person is exerting the only force on the object which causes motion, the work done equals the change in kinetic energy.

20
Q

An object is moving with 100 J of kinetic energy, and a frictional force acts on it, doing 50 J of work. What is the object’s final kinetic energy?

A

The object’s final KE is 50 J.

According to the work-energy theorem, the net work done on the object results in a change in its kinetic energy. Since the frictional force is the only force affecting motion, the work done equals the change in kinetic energy. Frictional forces can only do negative work, so the final kinetic energy is lowered.

21
Q

An object with mass m falls through a distance h. What is its final kinetic energy?

Assume no dissipative forces are present.

A

The object’s final KE is equal to mgh.

According to the work-energy theorem, the net work done on the object results in a change in its kinetic energy. Since gravity is the only force acting on the object, the change in kinetic energy simply equals the work done. Work = F * d, or, in this case, mg * h. You might also recognize this as the gravitational potential energy of the object before it fell.

22
Q

Define:

gravitational potential energy

A

An object’s gravitational potential energy (Ugr) is defined as the work that was needed to raise it to its present height above an arbitrary reference point.

On the MCAT, the reference point will always be ground level, unless otherwise stated.

23
Q

What is the gravitational potential energy of an object of mass m that is a height h above the surface of the Earth?

A

Ugr = mgh

This expression is identical to the work needed to raise the object that height, and is also equal to the kinetic energy the object will gain if it is allowed to fall freely to the ground.

24
Q

How does the gravitational potential energy of a mass change if its height above the surface of the Earth doubles?

A

The gravitational potential energy of the mass doubles.

Since gravitational potential energy of an object near Earth’s surface is given by Ugr = mgh, it is proportional to height above the ground. Changing the height changes the energy by the same amount.

25
Q

What is the potential energy of gravitational attraction between two objects of masses m1 and m2?

A

Ugr = -Gm1m2/r

G is the universal gravitational constant, and r is the distance between the centers of mass for the two objects.

This expression applies in all scenarios. In that way, it is different from Ugr=mgh, which only approximates that near the Earth’s surface gravitational acceleration is roughly constant (equal to g, ~10 m/s2).

26
Q

How does the gravitational potential energy between two masses change, if the distance between the two masses doubles?

A

The gravitational potential energy between the masses increases.

Be careful of signs! The general expression for gravitational potential energy, Ugr = -Gm1m2/r, is always negative. Increasing r makes the fraction smaller - in this case, less negative, reflecting an increase in potential energy.

27
Q

How can the potential energy of a spring be described?

A

A spring’s potential energy (Usp) is defined as the work needed to stretch or compress the spring from its equilibrium length to the current length.

On the MCAT, the spring’s equilibrium length will be defined as x = 0.

28
Q

What is a spring’s potential energy, if a mass m is attached and the spring is stretched to a distance x from equilibrium?

A

Usp = ½kx2

Here, x is the distance from equilibrium and k is the spring constant. There is no difference related to the sign for compression and expansion, since x2 will always be positive.

29
Q

How does the potential energy of a spring change if its extension from equilibrium doubles?

A

The potential energy of the spring increases by a factor of 4.

Since the potential energy of the spring (Usp = ½kx2) is proportional to the square of the displacement of the spring, stretching the spring increases the potential energy by the square of the length change.

30
Q

What is the force on a mass m, attached to a stretched spring, at a distance x from equilibrium?

A

F = -kx

Here, k is the spring constant (or force constant) of the spring (in N/m) and x is the distance from equilibrium. Notice that the negative sign means force will always act in the opposite direction of net displacement.

31
Q

If Spring 1 has twice the value of k that Spring 2 has, which spring must be moved the greater distance in order to create the same force?

A

Spring 2 (with the lower k) will need to be displaced further.

Since F=-kx and Spring 2 has 1/2 the k value of Spring 1, Spring 2 will need to move twice the distance to create the same value of F.

32
Q

Define:

total mechanical energy

A

The total mechanical energy of a physical system is the sum of the kinetic and potential energies of all the objects which make up the system.

Etotal = KEtotal + PEtotal

On the MCAT, you will rarely have to track more than one kinetic and one potential energy in any system.

33
Q

What specific energies constitute the total mechanical energy of a cannonball in flight?

A

The total mechanical energy consists of the kinetic energy from the cannonball’s velocity and the gravitational potential energy due to its height above the ground.

Assume the canonball is not rotating, unless explicitly mentioned. Rotational kinetic energy is rarely tested on the MCAT.

34
Q

What specific energies constitute the total mechanical energy of a mass oscillating on a horizontal spring?

A

The total mechanical energy consists of the kinetic energy from the mass’s velocity and the potential energy due to the extension or compression of the spring from equilibrium.

35
Q

What does the principle of conservation of energy state?

A

Conservation of energy states that, in the absence of dissipative forces, a system’s total mechanical energy is constant.

Dissipative forces such as friction or air resistance will decrease a system’s total mechanical energy.

36
Q

At the bottom of an initial hill, a roller coaster car is moving with a speed of v. Ignoring friction, what determines whether it can glide to the top of the next hill?

A

The car will reach the top of the next hill if its kinetic energy at the bottom Ki is greater than the gravitational potential energy will be at the top of the hill Uf.

Energy conservation states that total energy K+Ugr remains constant. At the bottom of the hill, potential energy is zero. If Ki > Uf, then the initial kinetic energy is sufficient to overcome the force of gravity and climb the hill. If Ki < Uf, the car will not make it to the top of the next hill.

37
Q

Define:

conservative force

A

A conservative force is one which does not dissipate mechanical energy.

When only conservative forces are acting on a system, the system’s total mechanical energy will stay constant.

38
Q

What are some common examples of conservative forces in physics?

A

The most common conservative forces on the MCAT are gravity, electrostatic and magnetic forces, and the restorative force of a stretched spring.

39
Q

A spring with a mass on each end is floating in space, and one mass is pushed towards the other to compress the spring and then released. How does the total mechanical energy of the compressed spring compare to the oscillating spring?

A

The total mechanical energy will be the same.

The compressed spring has only potential energy of position, and the oscillating spring can only have as much kinetic energy at equilibrium as was already present. Since no dissipative forces exist, and springs are conservative, total mechanical energy will remain constant.

40
Q

Define:

nonconservative force

A

A nonconservative force is one which dissipates mechanical energy.

When nonconservative forces are acting on a system, the system’s total mechanical energy will decrease.

41
Q

What are some common examples of nonconservative forces in physics?

A

The most common nonconservative forces on the MCAT are friction, air resistance, and fluid viscosity.

42
Q

A box is pushed at some speed across the floor by a force and then released. How does the total mechanical energy of the box at the point of release compare to the box at a later time?

Assume that this process occurs as it would in real life.

A

The total mechanical energy later will be less than when released.

The box itself only has kinetic energy due to velocity, but the dissipative force of friction acts between the box and the floor. Friction inhibits motion, so kinetic energy will be less the longer friction acts. Total mechnical energy, then, will also be less.