EXAM 4 (CHAPTERS 9, 10, 11)
A woman uses a pulley and a rope to raise a 16 kg weight to a height of 3 m . If it takes 4 s to do this, about how much power is she supplying?
120 W
The figure shows two blocks sliding on a frictionless surface. Eventually the smaller block overtakes the larger one, collides with it, and sticks. What is the speed of the two blocks after the collision?
5vi/4
Two friends are sitting in a stationary canoe. At t= 3s the person at the front tosses a sack to the person in the rear, who catches the sack 0.2 s later. Which plot in the figure shows the velocity of the boat as a function of time? Positive velocity is forward, negative velocity is backward. Neglect any drag force on the canoe from the water.
A
A small puck is sliding to the right with momentum p on a horizontal, frictionless surface, as shown in the figure. A force is applied to the puck for a short time and its momentum afterward is f. Which lettered arrow shows the direction of the impulse that was delivered to the puck?
B
Off center collisions
Can cause objects to go off in different angles
Where can kinetic energy go?
Can go into work or thermal energy and be considered "lost"
The experimenter from the video rotates on his stool, this time holding his empty hands in his lap. You stand on a desk above him and drop a long, heavy bean bag straight down so that it lands across his lap, in his hands. What happens?
He spins slower. The bean bag is not rotating before it contacts the experimenter, so (by conservation of rotational momentum) he must supply the rotational momentum required to make it spin at the same rate as his lap. Therefore, he ends up spinning slower.
Which of the following is an energy transfer?
Heat.
Moment of inertia equation
I = cmr^2 Constant (measures how close the mass is to the center) Mass Radius **Measures resistance to motions so the largest moment of inertia is where its moved to the rim
The thermal energy of a container of helium gas is halved. What happens to the temperature, in kelvin?
It decreases to one-half its initial value.
Motional inertia
Momentum
Conservation of momentum
No change in the total momentum of the system The net force is equal to zero which means its an isolated system
Elastic collision
No change in total momentum (conserved) and total kinetic energy No deformation; no energy given up as heat
Now, consider the collision between two happy balls described in Part A. How much of the balls' kinetic energy is dissipated?
None of it.
Inelastic collision
Objects stick together Ex. arrow through apple Only momentum is conserved Deformation is the main source of energy loss
Efficiency calculation
Output over input What you got out over what you put in
Power equation
P = DeltaE/Deltat Change in energy Time interval P = W/Deltat Work Time interval P = Fv Force Velocity
Understanding work done
Positive work indicates that an object has been acted on by a force that tranfers energy to the object, thereby increasing the object's energy. Negative work indicates that an object has been acted on by a force that has reduced the energy of the object.
Ramps
Potential energy is equal to kinetic energy mgh = 1/2mv^2 **Can lift more with a ramp
While keeping your food cold, your refrigerator transfers energy from the inside to the surroundings. Thus thermal energy goes from a colder object to a warmer one. What can you say about this?
The second law of thermodynamics applies in this situation, but it is not violated because the energy did not spontaneously go from cold to hot.
When the temperature of an ideal gas is increased, which of the following also increases?
The thermal energy of the gas.
The temperature of the air in a basketball increases as it is pumped up. This means that:
The total kinetic energy of the air is increasing and the average kinetic energy of each atom is increasing.
Elastic potential energy equation
U = 1/2kx^2 Restoring force Spring's displacement
Gravitational potential energy equation
U = mgh Mass Gravity Height The high on object is lifted the greater its gravitational potential energy
Collisions
When things bump into each other
An inventor approaches you with a device that he claims will take 90 J of thermal energy input and produce 270 J of electricity. You decide not to invest your money because this device would violate
both the first and second laws of thermodynamics.
If the time of a collision is reduced,
the force of the collision is increased.
A hockey puck sliding along frictionless ice with speed v to the right collides with a horizontal spring and compresses it by 1.0 cm before coming to a momentary stop. What will be the spring's maximum compression if the same puck hits it at a speed of 2v?
2.0 cm
Suppose we repeat the experiment from the video, but this time we use a rocket three times as massive as the one in the video, and in place of water we use a fluid that is twice as massive (dense) as water. If the new fluid leaves the rocket at the same speed as the water in the video, what will be the ratio of the horizontal speed of our rocket to the horizontal speed of the rocket in the video after all the fluid has left the rocket? (Ignore air resistance.)
2/3 The rocket's speed is proportional to the ratio of the fluid's mass to the rocket's mass.
A machine uses 1000 J of electric energy to raise a heavy mass, increasing its potential energy by 300 J. What is the efficiency of this process?
30%
Which has the largest momentum?
A heavy object moving at a high speed.
Cannon on ball
Ball will go farther than cannon Lighter object Bigger acceleration More work Bigger change in energy **Less massive objects have more KE
A red ball, initially at rest, is simultaneously hit by a blue ball traveling from west to east at 5 m/s and a green ball traveling east to west at 5 m/s . All three balls have equal mass. Afterward, the red ball is traveling south and the green ball is moving to the east. In which direction is the blue ball traveling?
Between north and west.
You and a friend each carry a 15 kg suitcase up two flights of stairs, walking at a constant speed. Take each suitcase to be the system. Suppose you carry your suitcase up the stairs in 30 s while your friend takes 60 s . Which of the following is true?
Both of you did the same work, but you expended more power.
First Law of Thermodynamics
Conservation on energy "Energy can be neither created nor destroyed; only transferred" The mechanical energy is conserved in an isolated system without friction Final total energy = initial total energy Delta E = Q - W Change in only thermal energy Heat Work
Change in kinetic energy
Delta E = Fd = work Force Change in distance Change in kinetic energy is work Larger the displacement the more work done Stronger the force the more work done
Change in momentum
Delta P = Ft = impulse Force Change in time Change is momentum is impulse Ex. swimming pool slows you down some before you hit so there's not as much force ***Momentum is a vector meaning it is conserved in the x and y directions (can be negative) ***An internal force cannot change the momentum If the graph is not constant must use area under the curve to find impulse An impulse given to an object changes the momentum
Heat change formula
Delta Q = mcDeltaT Mass Specific heat (given) Change in temp **Thermal energy must be in grams
Thermal energy equation
E = fDeltax Friction force Displacement
Coefficient of performance (COP)
Energy removed from the cold reservoir over Work required to preform transfer (hot - cold)
Heat
Energy transferred between two objects because of a temp difference between them Transferred from the warmer object to cooler object
Second Law of Thermodynamics
Entropy of an isolated system never decreases Increases or reaches equilibrium Efficiency
A giant "egg" explodes as part of a fireworks display. The egg is at rest before the explosion, and after the explosion, it breaks into two pieces, with piece B moving in the positive x direction. The masses of both pieces are 10 kg and 30 kg, shown traveling in opposite directions. During the explosion, is the magnitude of the force of piece A on piece B greater than, less than, or equal to the magnitude of the force of piece B on piece A? he component of the momentum of piece B is measured to be +500 kg⋅m/s after the explosion. Find the component of the momentum of piece A after the explosion.
Equal to -500 Momentum is always conserved M1v1 = M2v2
Hooke's Law
F = kx = ma Force Spring Constant Extension of material (length)
Test First and Second Laws of Thermodynamics
First: conservation of energy Input equals output plus waste Second: efficiency Output over input
Delta Pb = -Delta Pa Delta Pb + Delta Pa = 0
Follows third law (equal and opposite directions) Total momentum does not change *There is only so much momentum that the objects are passing around
Imagine that you replace the block in the video with a happy or sad ball identical to the one used as a pendulum, so that the sad ball strikes a sad ball and the happy ball strikes a happy ball. The target balls are free to move, and all the balls have the same mass. In the collision between the sad balls, how much of the balls' kinetic energy is dissipated?
Half of it.
Entropy
Increases as two systems with initially different temperature more toward thermal equilibrium When another form of energy is converted into thermal energy there is an increase in entropy
Suppose our experimenter repeats his experiment on a planet more massive than Earth, where the acceleration due to gravity is g=30 m/s2. When he releases the ball from chin height without giving it a push, how will the ball's behavior differ from its behavior on Earth? Ignore friction and air resistance.
It will take less time to return to the point from which it was released. The pendulum will swing back and forth more quickly (with a shorter period) because it is oscillating in a stronger gravitational field than that on Earth.
Kinetic energy equation
KE = 1/2mv^2 Mass Velocity **Kinetic energy of a rolling object is always greater than a non-rotating object moving at the same speed
As the projectile goes upward, what energy changes take place? At the top point of the flight, what can be said about the projectile's kinetic and potential energy? The potential energy of the object at the moment of launch __________.
Kinetic energy decreases; potential energy increases. Kinetic energy is at a minimum; potential energy is at a maximum. depends on the choice of the "zero level" of potential energy
Angular momentum equation
L = Iw Moment of inertia Angular velocity No net torque for the conservation of angular momentum
Thicker coils means:
Less movement Less stress Bigger restoring force Bigger acceleration
Center of mass
Might be easier to do it away from the center of mass Ex. lifting things
Linear Dynamics: Force Mass Velocity Linear momentum p = mv
Rotational Dynamics: Torque Moment of Inertia Angular velocity Angular momentum L = Iw
Newton's Laws that define: Impulse-momentum relationship Conservation of momentum
Second Law (Delta P = Ft is derived from F = ma) Third Law (Impulses are in equal and opposite directions so the change of momentum will be the same as well)
Greater impact velocity
Shorter impact time
Potential energy
Stored energy
Impulse forces
Strong, short forces Rapid change in momentum
A person walks 1 km , turns around, and runs back to where he started. Compare the energy used and the power during the two segments:
The energy used is the same for both segments, the power while running is greater.
Work
The process by which energy is transferred
Ideal gas
Thermal energy of an ideal gas is equal to the total kinetic energy of the moving atoms of the gas The temperature if an ideal fas is a measure of the average kinetic energy of the atoms that make up the gas
The cans have essentially the same size, shape, and mass. Which can has more energy at the bottom of the ramp? Ignore friction and air resistance.
They both have the same energy. The milk and the refried beans start out with the same amount of gravitational potential energy. Since mechanical energy is conserved in this experiment, both the milk and the refried beans must have the same amount of energy at the bottom of the ramp as well, but it may be divided differently between rotational kinetic energy and translational kinetic energy.
When the sun's light hits the earth, the temperature rises. Is there an entropy change to accompany this transformation?
Yes, the entropy increases.
Consider the video you just watched. The two pucks of equal mass did not move linearly (they came to a stop) after the collision due to the conservation of linear momentum. However, since the two pucks mutual center of mass does not coincide with either of the pucks velocity vectors, they have angular momentum. This becomes evident after the collision when due to conservation of angular momentum the two pucks spin around their mutual center of mass. Suppose we replace both hover pucks with pucks that are the same size as the originals but twice as massive. Otherwise, we keep the experiment the same. Compared to the pucks in the video, this pair of pucks will rotate
at the same rate. By doubling the mass but keeping the velocities unchanged, we doubled the angular momentum of the two-puck system. However, we also doubled the moment of inertia. Since L=I ω, the rotation rate of the two-puck system must remain unchanged.
A refrigerator is an example of a
heat pump.
The total momentum of a system is conserved
if no external forces act on the system.
If a system is isolated, the total energy of the system
is constant.
Momentum equation
p = mv mass velocity
If you raise an object to a greater height, you are increasing
potential energy.
