Work and Energy 2.1 - 2.3
Provide three methods for calculating the work done on or by a system?
1. W = Fdcos() (the dot product of the force and displacement vectors) 2. W = P x Delta V (The area under a pressure- volume curve) 3. Wnet = Delta K (the work-energy theorem)
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 lower peak velocity than Car B.
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 rating 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 may take longer for car A to reach a given velocity, both cars have unlimited maximum velocities according to the information given in the stem, eliminating choice D.
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 John. B. For John, the change in speed from the start of the jump to contracting the net is 20 m/s. C. John will experience a greater force upon impact than Sarah. D. The energy in this event is converted from potential to kinetic to elastic to kinetic.
A. Sarah will not bounce higher than Josh. Assuming the mechanical energy is converted, 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 logistic, both individuals should return to the same starting height. Josh starts with U = mgh ~ 80kg x 10m/s^2 x 20m = 16000J of potential energy. At the moment he hits the net, all of this potential energy has been converted into kinetic energy. Therefore, K = 1/2 mv^s --> v = sqr (2K/m) sqr(2 x 16000/ 80) = sqr(400) = 20m/s I got it wrong, i used the F = ma but we are not talking about acceleration, it does not have the same units, so make sure you do not use it again.
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
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 then 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.
A pulley system (with 6 pulleys) has an efficiency of 80 percent. A person is lifting a mass of 200 kg with the pulley. Find, A. The distance through which the effort must move to raise the load a distance of 4m. B. The effort required required to lift the load C. The work done by the person lifting the load through a height of 4m
A. For the load to move through a vertical distance of 4m, all six of the supporting ropes must be shorten by 4 m also. This may only be accomplished by pulling 6 x 4 = 24 m of rope through the set up. B. To calculate the effort required, the equation for efficiency should be used. The load is the weight of the object being lifted and is equal to the mass of the object times the acceleration due to gravity. The effort distance is calculated in part A, is 24m C. for here use the other equation for Work when dealing with efficiency. W in = (effort)(effort distance)
As the effort decreases in a pulley system, what happens to the effort distance to maintain the same work output?
As the effort (required force) decreases in a pulley system, the effort distance increases to generate the same amount of work Think of the bottom part of the equation for efficiency. If (effort) goes down (its multiplicator) the effort distance must increase to compensate and have the same output work.
As the length of an incline plane increases, what happens to the force required to move an object the same displacement?
As the length of an inclined plane increases, the amount of force necessary to perform the same amount of work (moving the object the same displacement) decreases.
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 motion 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
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 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 force acting on the parachutist, making statement II false.
In the pulley system shown below, which of the following is the closest to the tension force in each rope if the mass of the object is 10kg and the object is accelerating upwards at 2 m/s? A. 50 N B. 60 N C. 100 N D. 120 N
B. From the diagram, notice that there are two tensions forces pulling the mass up. The net force for this system (Fnet) is equal to 2T - mg. Not we can use Neuton's seconds law: Fnet = ma 2T - mg = ma T = m(a + g) /2 = (10kg)(2m/s^2 + 10m/s^2) / 2 5 x 12 = 60N
Mechanical advantage and efficiency are both ratios. Which of the following is true regarding the quantities used in these ratios? A. Mechanical advantage compares values of work; efficiency compares values of power B. Mechanical advantage compares values of forces; efficiency compares values of work C. Mechanical advantage compares values of power; efficiency compares values of energy D. Mechanical advantage compares values of work; efficiency compares values of forces.
B. Mechanical advantage is a ratio of the output force generated given a particular input force. Efficiency is the ratio of the useful work performed by a system compared to the work performed on the system. D
A 200 kg experimental car can accelerate from 0 to 30m/s in 6 s. What is the average power of the engine needed to achieve this acceleration? A. 150W B. 150kW C. 900W D. 900kW
B. The work done by the engine is equal to the change in kinetic energy of the car: W = Delta K = 1/2 m (V^2 final -V^2 initial) = 1/2(2000kg)(900 m^2/s^2 - 0) = 900,000J. The average power therefore is P = W/t = 900,000 / 6 s = 150,000W = 150kW 30^2 = 900
Which of the following best characterizes the work-energy theorem? A. The work done by any force is proportionally 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
B. The work-energy theorem relates the total work done on an object by all forces to the kinetic energy experienced by the same object. While the work done by a force is indeed proportional to the magnitude of the fore, 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 eliminated Choice D.
A weight lifter lifts a 275kg barbell from the ground to a height of 2.4m. How much work has he done in lifting the barbell, and how much work is required to hold the weight at the height? A. 3234 J and 0 J, respectively B. 3234 J and 3234J, respectively C. 6468 J and 0 J, respectively D. 6468 J and 6468 J, respectively
C. Because the weight of the barbell (force acting downward) is mg = 275kg x 10 m/s^2, or about 2750N, it follows that the weightlifter must exert an equal and opposite force of 2750 N on the barbell. The work done in lifting the barbell is therefore W = FdCos() = (2750N)(2.4m)(cos o) ~= 7,000 J. Using the same equation, it follows that the work done to hold the barbell in place is W = Fdcos() = (2750)(0M)(cos())= 0 J. Because the barbell is held in pace and there is not displacement, the work done is zero. This is closes to choice C.
If the gravitational potential energy of an object has doubled in the absence of nonconservative forces, which of the following must be true, assuming the total mechanical energy of the object is constant? A. The object has been lifted to twice its initial height. B. The kinetic energy of the object has been halved. C. The kinetic energy has decreased by the same quantity as the potential energy has increased. D. The mass of the object has doubled.
C. In the absence of nonconservatie forces, all changes potential energy must be met by an equal change in kinetic energy. Note that it is the difference in potential energy that is the same as the difference in kinetic energy, not the proportionality, eliminating Choice B. Both choices A and D could be true statement but do not necessarily have to be- the objects mass could have been quadrupled while its height was halved. I got it wrong, two answer A and B seemed correct, which made them both wrong as the answer was other one. keep it in mind for test day.
A tractor pulls a log with a mass of 500 kg along the ground for 100m. The rope (between the tractor and the log) makes an angle of 30 degrees with the ground and is acted on by e tensile force of 5000N. How much work does the tractor perform in this scenario? (Note: sin30 = .5, cos30 = .866, tan30 = .577) A. 250 kj B. 289 kj C. 433 kj D. 500 kj
C. The work done by the tractor can be calculated from the equation: W = FdCos() = (5000N)(100m)(Cos30) = = (5000N)(100m)(.866) ~= 5000 x 80 = 400,000 = 400kJ. This is closest to choice C.
5 m^3 of a gas are brought from an initial pressure of 1 kPa to a pressure of 3kPa through an isochoric process. During this process, the work performed by the gas is: A. -10 kJ B. -10 J C. 0 J D. + 10 kJ
C. An isochoric process, by definition, is one in which the gas system undergoes no change in volume. If the gas neither expands nor is compressed, then no work is performed. Remember that work in a thermodynamic system is the area under a P-V curve; if the change in volume is 0, then the area under the curve is also 0.
Which if the following is a conservative force? A. Air resistance B. Friction C. Gravity D. Convection
C. Gravity is a conservative force because it is pathway independent and it does not dissipate mechanical energy. Air resistance and friction are nonconservative forces that dissipate energy thermally. Convection is not a force, but a method of heat transfer.
A 40 kg block is resting at a height of 5m 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 2m, assuming negligible air resistance? A. 0 J B. 400 J C. 800 J D. 2000 J
D. Assuming negligible air resistance, conservation of energy states that total mechanical energy of the block is constant as it falls. At the starting height of 5m, the block only has potential energy equal to U = mgh ~~ (40kg)(10,/s^2)(5m) = 2000 J. Because the kinetic energy at this point is 0 J, the total mechanical energy is 2000 J at any point during the blocks descent.
A massless spring initially compressed by a displacement of two centimeters is now compressed by four centimeters. How has the potential energy of this system changed? A. The potential energy has not changed B. The potential energy has doubled C. The potential energy has increased by two joules D. The potential energy has quadrupled
D. Elastic potential energy, like kinetic energy, is related to the square of another variable, as shown by the equation U = 1/2 kx^2. Increasing the displacement by a factor of 2 increases the potential energy by a factor of 2^2 = 4.
How would you find the total amount of work done in a P-V graph that has a shape of a triangle and a rectangle?
I would use the formula to find the area of a triangle. 1/2 Delta V x Delta P the area under the curve will be the work done.
What happens in an isovolumetric or isochoric precess?
If volume stays constant as pressure changes ( V = O), then no work is done because there is no area to calculate under the curve. For a process i which pressure changes but volume stays constant there is no work done and the process is called Isovolumetric or Isochoric.
Define Kinetic Energy
Kinetic energy is the energy of motion. It is related to the mass of an object as well as its speed squared.
What is the equation of power? What are the units of power?
P = power W = work (which is equal to Delta E, the change in energy) t = is the time over which the work is done The units of power is the WATT 1 Watt = J/s
Define Potential Energy
Potential energy is energy associated with a given position or intrinsic property of a system; it is stored in gravitational, electrical, elastic, or chemical forms.
What happens in an isobaric process?
Pressure remains constant as volume changes (that is P = 0), then the area under the curve is a rectangle of length p and the with of Delta V. For processes for which pressure remains constant is called an Isobaric process
What accounts for the difference between work input and work output in a system that operates at less than 100% efficiency?
The decrease in work output is due to nonconservative (friction) or external forces that generate or dissipate energy.
What are the units for work? How are work and energy different?
The units for work is the Joule, which is also the unit of energy. Work and energy are related concepts. By performing work, the energy of a system is changed. Work along heat, is a form of energy transfer.
What is work energy theorem and what is its significance? How would you show the work-energy theorem in mathematical terms?
The work energy theorem is an important relationship between Work and Energy, it offers a direct relationship between work done by all the forces acting on an object and the change in kinetic energy. final minus initial for the formula.
what is the equation for energy when there is nonconservative forces present?
W nonconcervative = Delta E = Delta U + Delta K
What does it mean for a device to provide mechanical advantage?
When a device provides mechanical advantage, it decreases the input force required to generate a particular output force. Generally, this is accomplished at the expense of increased distance over which the force must act.
What is the equation for work done in a piston? P-V graph.
Work can be calculated by multiplying the Pressure times the volume. This gives us an area, the are under the curve is equal to the amount of work done.
what is the difference between conservative forces and nonconservative forces?
conservative forces (such as gravity and electrostatic forces) conserve mechanical energy. Nonconservative forces (such as friction and air resistance) dissipate mechanical energy as thermal or chemical energy. Conservative forces are those that are path independent. Nonconservative forces are pathway dependent.
What is the equation for work? this formula involves force and distance.
work is equal to the applied force times the distance of displacement, and cos() is the angle between the applied force vector and the displacement vector.
