Chapter 2: Work and Energy
D (Assuming negligible air resistance, conservation of energy states that the total mechanical energy of the block is constant as it falls. At the starting height of 5 m, the block only has potential energy equal to U = mgh = 40 kg * 10 m/s^2 * 5 m = 2000 J. Because teh kinetic energy at this point is 0 J, the total mechanical energy is 2000 J at any point during the block's descent.)
A 40 kg block is resting at a height of 5 m off the ground. If the block is released and falls to the ground, which of the following is closest to its total mechanical energy at a height of 2 m, assuming negligible air resistance? A.) 0 J B.) 400 J C.) 800 J D.) 2000 J
B (The minimum force required to push the block can be found by applying the formula F = mgsin(theta); mg represents the weight of the object which is 100 N and sin(theta) can be found by taking the length of the opposite over the hypotenuse which is 10/20. Therefore, F = 100N * 1/2 = 50 N. To raise the block vertically, an upward force equal to the object's weight would have to be generated so F would be equal to 100 N. Thus, the same amount of work is required in both cases, but twice the force is needed to raise the block vertically compared with pushing it up the incline.)
A block weighing 100 N is pushed up a frictionless incline over a distance of 20 m to a height of 10 m as shown in the figure. How much more force is needed to raise the block vertically compared with pushing it up the incline? A.) 1/2 B.) 2 C.) 4 D.) 8 E.) The same force is needed
A (Horsepower is a unit of power, as evidenced by the name and the conversion factor given in the question stem. Power is a rate of energy expenditure over time. Given unlimited time, both cars are capable of unlimited increases in (kinetic) energy, meaning that they have unlimited maximum velocities. The fact that Car B has a higher power means that it will reach any given velocity faster than Car A, eliminating choice B. There is not enough information to make any judgements on the efficiency of the cars, eliminating choice C. While it takes longer for Car A to reach a given velocity, both cars have unlimited maximum velocities according to the information give in the stem, eliminating choice D.)
A consumer is comparing two new cars. Car A exerts 250 horsepower, while Car B exerts 300 horsepower. The consumer is most concerned about the peak velocity that the car can reach. Which of the following statements would best inform the consumer's decision? Note: 1 horsepower = 745.7 W) A.) Car A and Car B both have unlimited velocities, ignoring nonconservative forces. B.) Car A will reach its peak velocity more quickly than Car B. C.) Car A will dissipate less energy to the surroundings than Car B. D.) Car A will have a lower peak velocity than Car B.
B (At terminal velocity, the force of gravity and force of air resistance are equal in magnitude, leading to translational equilibrium. Thus, statement I is true. If these forces have the same magnitude and act over the same displacement, then the work performed is the same as well, making statement III true. Even though the net force is equal to zero, there are still forces acting on the parachutist, making statement II false.)
A parachutist jumps from a plane. Beginning at the point when she reaches terminal velocity (constant velocity during freefall), which of the following is/are true? I. The jumper is in translational equilibrium. II. The jumper is not being acted upon by any forces. III. There is an equal amount of work being done by gravity and air resistance. A.) I only B.) I and III only C.) II, and III only D.) I, II, and III
A (In uniform circular motion, the displacement vector and force vector are always perpendicular; therefore, no work is done. Potential energy is constant for an object in uniform circular motion, whether it is the gravitational potential energy of a satellite orbiting the Earth or the electrical potential energy of an electron orbiting the nucleus of an idealized atom. In both cases, potential energy does not change and does not depend on the position of the object around the circle, eliminating choice D.)
During uniform circular motion, which of the following relationships is necessarily true? A.) No work is done. B.) The centripetal force does work. C.) The velocity does work. D.) Potential energy depends on position of the object around the circle.
positive (Work is done BY the system.)
For a gas system contained in a cylinder with a movable piston, we can analyze the relationship between pressure, volume, and work. When the gas expands, it pushes up against the piston, exerting a force that causes the piston to move up and the volume of this system to increase. In this case, is work said to be positive or negative?
negative (Work is done ON the system.)
For a gas system contained in a cylinder with a movable piston, we can analyze the relationship between pressure, volume, and work. When the gas is compressed, the piston pushes down on the gas, exerting a force that decreases the volume of the system. In this case, is work said to be positive or negative?
U=mgh
Give the formula for gravitational potential energy.
K=1/2mv^2
Give the formula for kinetic energy.
datum
Gravitational potential energy depends on an object's position with respect to some level identified as the ______ ("ground" or the zero potential energy position). This zero potential energy position is usually chosen for convenience.
A (Sarah will not bounce higher than Josh. Assuming that mechanical energy is conserved, Sarah and Josh will start with a given amount of potential energy, which is converted into kinetic energy, then elastic potential energy, then kinetic energy again with no loss of energy from the system, eliminating choice D. By this logic, both individuals should return to the same starting height. Josh starts with U=mgh ~ 80 kg x 10 m/s^2 x 20 m = 16,000 J of potential energy. At the moment he hits the net, all of his potential energy has been converted into kinetic energy. Therefore, K = 1/2mv^2 --> v=sqrt(2K/m) = sqrt(2 x 16,000 / 80) = 20 m/s, eliminating choice B. Josh will experience a greater force upon impact because the net exerts a force proportional to weight; the higher the weight, the larger the force exerted by the net, eliminating choice C.)
Josh, who has a mass of 80 kg, and Sarah, who has a mass of 50 kg, jump off a 20 m tall building and land on a fire net. The net compresses, and they bounce back up at the same time. Which of the following statements is NOT true? A.) Sarah will bounce higher than Josh. B.) For Josh, the change in speed from the start of the jump to contacting the net is 20 m/s. C.) Josh will experience a greater force upon impact than Sarah. D.) Th energy in this event is converted from potential to kinetic to elastic to kinetic.
inclined plane, wedge, wheel and axle, lever, pulley, screw
List the six simple machines that provide the benefit of mechanical advantage.
force, distance (For example, sloping inclines, such as hillsides and ramps, make it easier to lift objects because they redistribute the required work over a larger distance, decreasing the required force.)
Mechanical advantage makes it easier to accomplish a given amount of work because the ______ necessary to accomplish the work is reduced; the ______, however, is increased by the same factor (assuming 100% efficiency).
first law of thermodynamics
The ______ ______ ______ ______ accounts for the conservation of mechanical energy, which posits that energy is never created no destroyed - it is merely transferred from one form to another.
effort
The ______ is the input force of a simple machine, which acts over a given ______ distance to determine the work input of the simple machine (same word for both blanks).
load
The ______ is the output force of a simple machine, which acts over a given ______ distance to determine the work output of the simple machine (same word for both blanks).
work-energy theorem
The ______-______ ______ states that when net work is done on or by a system in a mechanical application, the system's kinetic energy will change by the same amount: Wnet = ΔK = Kf - Ki. NOTE: In more general applications, the work done on or by a system can be transferred to other forms of energy as well.
isobaric (Pressure remains constant as volume changes and work can be calculated as W = PΔV.)
The curve depicted in the figure describes a(n) ______ process.
isovolumetric (also accept isochoric; volume stays constant while pressure changes and no work is done.)
The curve depicted in the figure describes a(n) ______ process.
load
The figure depicts a two-pulley system. What term is used to describe the block?
effort (Since each rope supports 1/2 of the block's total weight, only half the effort is required to lift the block. This decrease in effort is the mechanical advantage provided by the pulley.)
The figure depicts a two-pulley system. What term is used to describe the force that is required to lift the block?
load distance
The figure depicts a two-pulley system. What term is used to describe the height at which the object must be lifted?
effort distance (Since each rope supports 1/2 of the block's total weight, one must pull through an effort distance equal to twice the displacement.)
The figure depicts a two-pulley system. What term is used to describe the length of rope necessary to lift the object to a certain height?
work-energy theorem (Wnet = ΔK = Kf - Ki)
The following example supports what theorem? You press the brake pedal in your car. The brake pads exert frictional forces against the rotors, which are attached to the wheels. These frictional forces do work against the wheels, causing them to decelerate and bring the car to a halt. The net work done by all these forces is equal to the change in kinetic energy of the car.
mechanical energy
The total ______ ______ of a system is the sum of its kinetic and potential energies: E = U + K.
False (The total mechanical energy equation E = U + K accounts for potential and kinetic energies but not for other forms of energy, such as thermal energy that is transferred as a result of friction (heat). This being said, there is no violation of the first law of thermodynamics since it accounts for all forms of energy.)
True or False: According to the conservation of mechanical energy, the total mechanical energy will always remain constant.
True (Displacement is pathway independent so the actual distance traveled from the initial to final position does not matter, assuming all forces are conservative.)
True or False: Applying a lesser force over a greater distance to achieve the same change in position accomplishes the same amount of work.
False (Elastic forces, such as those created by springs, are nearly conservative and can be approximated to be conservative in some cases. In actuality, springs heat up as they move back and forth due to the friction between the particles of the spring material, making elastic forces nonconservative.)
True or False: Elastic forces are conservative.
True (Conservative forces are path independent and do not dissipate the mechanical energy of a system.)
True or False: If only conservative forces are acting on an object, the total mechanical energy will remain constant.
False (If pressure remains constant, ΔP = 0, then the area under the curve is a rectangle of length P and width ΔV.)
True or False: If pressure stays constant as volume changes, then no work is done.
True (Work can be expressed as the volume under a P-V curve. If ΔV = 0, then work is equal to 0.)
True or False: If volume stays constant as pressure changes, then no work is done.
False (Kinetic energy is related to speed, not velocity. An object has the same kinetic energy regardless of the direction of its velocity vector: K = 1/2 mv^2)
True or False: Kinetic energy is dependent on velocity.
True (Work is a dot product between force and displacement; as such, it is a function of the cosine of the angle between the vectors. Cosine of an angle perpendicular to the displacement gives a value of 0.)
True or False: Only forces (or components of forces) parallel or antiparallel to the displacement vector will do work, that is transfer energy.
True (The work-energy theorem states that when net work is done on or by a system, the system's kinetic energy will change by the same amount. In the case of the first law of thermodynamics, the change in internal energy (ΔU) is equal to the heat transferred into the system (Q) minus the mechanical work done by the system (W).)
True or False: The first law of thermodynamics is essentially a reiteration of the work-energy theorem.
True (Wnonconservative = ΔE = ΔU + ΔK)
True or False: The work done by nonconservative forces only will be exactly equal to the amount of energy transformed into another form of energy that is not accounted for in the mechanical energy equation.
True (The load determines the necessary output force. From the output force and mechanical advantage, we can determine the necessary input force, or effort.)
True or False: When considering simple machines, load and effort are both forces.
False (Although work has the SI unit of the joule which is the same for all forms of energy, work is not actually a form of energy itself, but a process by which energy is transferred from one system to another. The other form of energy transfer is heat.)
True or False: Work is just another form of energy.
gravitational, electrostatic
What are two common examples of conservative forces that are frequently encountered on the MCAT?
Wnonconservative = ΔE = ΔU + ΔK (Apply the energy equation for a nonconservative system.)
What equation should you use to answer the following question? A baseball of mass 0.25 kg is thrown in the air with an initial speed of 30 m/s, but because of air resistance, the ball returns to the ground with a speed of 27 m/s. Find the work done by air resistance.
Wnet = kf - ki (Apply the work-energy theorem; another solution would be using kinematics and determining the maximum height of the ball: W = Fd cos(theta).)
What equation should you use to answer the following question? A lead ball of mass 0.125 kg is thrown straight up in the air with an initial velocity of 30 m/s. Assuming no air resistance, find the work done by the force of gravity by the time the ball is at its maximum height.
equilibrium, elastic potential, spring constant
When a spring is stretched or compressed from its ______ length, the spring has ______ _____ energy, which can be determined by U=1/2kx^2. Where U is the potential energy, k is the ______ ______ (a measure of the stiffness of the spring), and x is the magnitude of displacement.
expands
When work is done by a system, meaning the gas ______, the work is said to be positive.
compresses
When work is done on a system, meaning the gas ______, the work is said to be negative.
B (The work-energy theorem relates the total work done on an object by all forces to the change in kinetic energy experienced by the same object. While the work done by a force is indeed proportional to the magnitude of the force, it is also proportional to the displacement of the object, eliminating choice A. The change in kinetic energy is equal - not proportional - to the total work done on the object; further, it is the net force, not any force, that relates to the work done on an object, eliminating choice C. Finally, the change in kinetic energy of the object is equal to the work done by all of the forces acting on the object combined, not just the applied force, which eliminates choice D.)
Which of the following best characterizes the work-energy theorem? A.) The work done by any force is proportional only to the magnitude of that force. B.) The total work done on any object is equal to the change in kinetic energy for that object. C.) The work done on an object by any force is proportional to the change in kinetic energy for that object. D.) The work done by an applied force on an object is equal to the change in kinetic energy of that object.
pressure-volume (P-V)
Work may also be expressed as the area under a ______-______ curve.
dot, cosine
Work may be expressed as the ______ product of force and displacement, or the product of force and distance traveled within the ______ of the angle between the two.
Mechanical advantage
______ ______ is the factor by which a simple machine multiplies the input force to accomplish work. In other words, the ratio of magnitudes of the force exerted on an object by a simple machine (Fout) to the force actually applied on the simple machine (Fin).
Kinetic
______ energy is energy associated with the movement of objects.
Potential
______ energy is energy stored within a system. It exists in gravitational, elastic, electrical, and chemical forms.
Nonconservative
______ forces are path dependent and cause dissipation of mechanical energy from a system as thermal or chemical energy; examples include friction, air resistance, and viscous drag.
Conservative
______ forces are path independent and do not dissipate the mechanical energy of a system.
Work
______ is a process by which energy is transformed from one system to another.
Energy, joules
______ is the property of a system that enables it to do something or make something happen, including the capacity to do work. The SI units for all forms are ______.
Power
______ is the rate at which work is done (W/t) or energy is transferred (ΔE/t) ; the SI unit for this quantity is the watt (W) or J/s.
Efficiency
______ is the ratio of the machine's work output to work input when nonconservative forces are taken into account.