Physics Exam 3
Elastic collision
A collision in which colliding objects rebound without lasting deformation or the generation of heat. No KE is lost, momentum is conserved
Inelastic collision
A collision in which the colliding objects become distorted, generate heat, and possibly stick together Momentum is conserved, some KE is lost
Identify all the non-inertial reference frames from the list below: 1. Feeling pushed forward when a car brakes 2. Standing in line and throwing a ball to your friend riding a carousel 3. Watching a cell phone be pushed off the dashboard to the right while your car turns left 4. Playing on the merry-go-round at the playground, and holding on tightly because you feel like you're about to be flung off 5. Pushing off from the ice to begin a speed skating race
#1, #3, and #4
At what angle should force be applied to a lever arm to achieve minimum torque?
0 degrees
1 J
1 kg m^2/s^2 or N m
How much work is done when a weightlifter lifts a 200N200N barbell from the floor to a height of 2m?
400J Remember that when force and displacement are non-zero, the work done will be zero only when force and displacement are acting in perpendicular directions.
What is a perfect inelastic collision?
A perfect inelastic collision is one in which objects stick together after impact, and their internal energy is not conserved.
Two different size boxes made of the same material are located on a flat surface. If Box A has been filled so that it only has ⅓ the mass of Box B, but it has twice the bottom surface area what is the relationship between the forces that must be used to overcome the friction generated by each box to move them parallel along the floor?
Box B requires 3 times as much force to overcome friction. Box B requires 3 times as much force to overcome friction. Static friction only depends on the coefficient of static friction and the normal force which is calculated as N = mg in this situation.
Can the centripetal force on an object undergoing uniform circular motion do work?
No b/c it is at constant speed so the energy associated is the same and height isn't changing
Most electrical appliances are rated in watts. Does this rating depend on how long the appliance is on?
No
True or False: A woman in a store buys a 100-W100-W lightbulb. This means that the bulb will convert 100-W100-W of electrical power to visible light.
False
How is work affected by acceleration?
Fnet causes acceleration which increases velocity=increase in kinetic energy and therefore work on object causes an increase in KE
In the equation 𝑝1+𝑝2=𝑝′1+𝑝′2p1+p2=p1′+p2′ for the collision of two objects, what is the assumption made regarding the friction acting on the objects?
Friction is zero.
Non-conservative forces
Frictional forces, air resistance, tension, normal force, propulsion of a motor
Torque
How effective a force (F) is at causing rotation about an axis A force is more effective if it is farther from axis (r) A force is most effective when it is perpendicular to r T=rFsin(theta)=rFperpendicular (lever arm) 180°-no torque 90°-most torque
You run up 35 flights of stairs and run back down them. Have you done work?
No
Static equilibrium
No acceleration Fnet=0 Tnet=0 about EVERY possible axis of rotation
Unstable (static equilibrium)
If the object is pushed slightly it will not return to the initial position
Stable (static equilibrium)
If the object is pushed slightly it will return to the initial position
How does work of non-conservative forces affect energy?
If there are non-conservative forces, MEpoi1+Wnc=MEpoi2 or Wnc=deltaME
Tennis racquets have "sweet spots." If the ball hits a sweet spot then the player's arm is not jarred as much as it would be otherwise. How does the "sweet spot" change the impact time of the ball?
It increases impact time
Mechanics sometimes put a length of pipe over the handle of a wrench when trying to remove a very tight bolt. How does this make it easier for the mechanic to remove the bolt?
It increases the torque the mechanic can apply, without the need to exert a greater force.
When you push a door closer to the hinges, why does it open more slowly?
It opens slowly, because the lever arm is shorter so the torque is less.
Cars these days have parts that can crumple or collapse in the event of an accident. What is the advantage of this?
It reduces injury to the passengers by increasing the time of impact. Increasing the time of impact decreases the force acting, as obtained from Newton's second law of motion.
Two surfaces in contact are moving slowly past each other. As the relative speed between the two surfaces in contact increases, what happens to the magnitude of their coefficient of kinetic friction?
It remains constant and is independent of the relative motion.
Energy conservation
ME=PE+KE Non-conservative forces convert ME to other forms of energy If there are no non-conservative forces (Wnc=0) then ME is conserved (MEpoi1=MEpoi2)
What two quantities are crucial to quantifying the translational kinetic energy of an object?
Mass and speed
Two steel balls collide and bounce apart in an isolated system. If the final kinetic energy is less than the initial kinetic energy, which of the following is true?
Momentum is conserved in this inelastic collision
What is the difference between momentum and impulse?
Momentum is the product of mass and velocity. Impulse is the change in momentum.
Conservation of momentum
Momentum of a system remains constant when there are no net external forces acting on it. Momentum is always conserved during a collision
A ball is hit by a racket and its momentum changes. How is momentum conserved in this case?
Momentum of the system is conserved if the momenta of the racket and the player are also considered. The system should also include the momentum of the player; only then is the momentum conserved for the system.
If force and displacement are in opposite directions, will work be positive or negative?
Negative
A friend slides a box along a flat floor to you, which you slow by applying a force at a 30° angle. Is the work you do to slow the box positive or negative? If you instead placed a book directly on top of the box as it passed you, what can you say about the work done by the book?
Negative work, No work done
Is it possible for the sum of kinetic energy and potential energy of an object to change without work having been done on the object? Explain.
No, because the work-energy theorem states that work done on an object is equal to the change in kinetic energy, and change in KE requires a change in velocity. It is assumed that mass is constant. It is not possible for the kinetic energy of an object to change without work having been done on the object. The work-energy theorem states that work done on an object is equal to the change in kinetic energy.
Can F_Table on box do work?
No, box is just sitting there and not gaining energy
Suppose a train is moving along a track. Is there a single, correct reference frame from which to describe the train's motion?
No, there is not a single, correct frame of reference because motion is a relative term.
If you and a friend are standing side-by-side watching a soccer game, would you both view the motion from the same reference frame?
No, we would both view the motion from different reference points because motion is viewed from two different points; the reference frames are similar but not the same. The reference frames are similar but not same. The two reference frames are located at two different points, hence the motion described by each frame will be slightly different.
Spring potential energy
PE=1/2kx^2 Always positive
Is there a situation in which a force exerted on an object does no work on the object?
Pushing any fixed object (object has to move, accelerate along direction of movement)
Two springs are attached to two hooks. Spring A has a greater force constant than spring B. Equal weights are suspended from both. Which of the following statements is true?
Spring B will have more extension than spring A. Remember that the force constant indicates the stiffness of the spring, so spring A will be stiffer. Therefore, it is not correct to state that spring A will have more extension.
Which of the following systems is in stable equilibrium? 1) a skateboard at rest at the bottom of a U-shaped ramp 2) a ball at rest on the edge of a table 3) a quarter, at rest, balanced on its edge
System 1
How can you maximize the torque applied to a given lever arm without applying more force?
The force should be applied perpendicularly to the lever arm as far as possible from the pivot point. Since the applied force is the same, torque can be increased by increasing the distance from the point of application of the force to the pivot.
Neglecting friction, what factor affects the final speed of an object sliding down a ramp?
The height of the ramp
What is the statement for Newton's second law in terms of momentum?
The net external force equals the change in momentum of a system divided by the time during which it changes.
Momentum
The product of an object's mass and velocity p=mv Vector quantity kg m/s
A small force and a large force impart the same change in momentum. What does this imply about the time interval over which each force acts?
The time interval is greater for the small force.
You hold a barbell in a horizontal position. The barbell's center of mass is exactly mid-way between your two hands. A friend walks up and attaches a weight on the end near your left hand. How does the torque on the bar exerted by your left hand compare to the torque on the bar from your right hand if the bar remains horizontal and at rest?
The torque from the left hand is greater than the torque from the right hand.
Three pendulums all have the same length and start from the same height. The first pendulum is very light and has a mass of 67 g. The second pendulum has a mass of 1.5 kg. The final pendulum has a mass of 3.3 kg. Assume that the effects of air drag are negligible. Which pendulum attains the highest velocity?
They will all attain the same maximum velocity
Net torque
Tnet=Tccw-Tcw
True or False: A car runs out of gas and coasts down one hill and up another until it comes to a stop. The point at which the car stops is lower than the point at which it started coasting because part of the original potential energy has been converted to a quantity of heat, which makes the tires feel warm.
True
True or False: In an inelastic collision, kinetic energy is not conserved.
True
True or False: The energy increase of an object acted on only by a gravitational force is equal to the product of the object's weight and the distance the object falls.
True
While carrying a heavy box, a boy walks horizontally across a room at a constant speed. True or False: The boy is doing no work on the box.
True
True or False: To calculate the speed of the pebble dropped from the cliff as it hits the ground requires you to only know the height of the cliff and acceleration due to gravity.
True Conservation of mechanical energy of the system gives 1/2𝑚𝑣^2=𝑚𝑔ℎ. 1/2mv^2=mgh. The mass 𝑚m cancels, so 𝑣=(2𝑔ℎ)1/2v=(2gh)^1/2, and 𝑔g and ℎh are known.
True or False: For a conservative force, you can determine the work done by just knowing the initial and final position
True; work done by a conservative force around a closed path is zero
True or False: A non-conservative force requires knowing the path of motion.
True; work done depends on the path
Potential energy and work
Wc=-deltaPE +work -PE
Define work for one-dimensional motion.
Work is defined as the product of the force and the distance. The product of force and the distance over which the force was acting will give the work done.
A basketball is dropped and each time it bounces, the maximum height it reaches becomes smaller and smaller. Is this an example of a system in which nonconservative forces are acting?
Yes
Carlos is deciding if he will climb a mountain in a zigzag path or straight up the side, starting from rest and ending at rest. Neglecting friction and disregarding other factors, will his potential and kinetic energy consumption be the same for both paths?
Yes
Imagine a roller coaster, with an initial speed of 5m/s5m/s downhill, descends 20m20m in height. Now suppose the roller coaster, with an initial speed of 5m/s5m/s uphill, coasts uphill, stops, and then rolls back down to a final point 20m20m below the starting point. Would the final speed be the same in these two cases? Assume friction is negligible.
Yes
Two objects having equal masses and velocities collide with each other and come to a rest. Is momentum conserved in this case?
Yes
You carry a box from one table to another table in the room. Did you do work on the box?
Yes if the second table is taller
Is it possible to do work on an object without changing the kinetic energy of the object?
Yes, it is possible by raising the object to a greater height without acceleration. Work can change the KE of an object, as described by the work-energy theorem, but it can also change the PE of an object by raising it to a greater height at a constant speed (that is, without acceleration)
A ball is at rest at the highest point on a hill. Is the ball in equilibrium, and if so, what kind of equilibrium?
Yes, the ball is in unstable equilibrium.
Perfectly inelastic collision
a collision in which two objects stick together after colliding a lot of KE is lost, momentum is conserved
Why do we use average force while solving momentum problems? How is net force related to the momentum of the object?
because forces are usually not constant over a period of time, and net force acting on the object is equal to the rate of change of the momentum
How does a car airbag reduce the impact of the person driving?
by increasing the time over which the momentum of the driver changes Newton's second law of motion confirms that increasing the time over which the momentum changes will result in lesser external force.
Impulse
change in momentum deltap=Fnetdeltat I=deltap I=FnetdeltaT Vector quantity
After traveling along a path, a toy car's final velocity is 10m/s. If the car had traveled along the alternate path, as shown in the diagram, would its final velocity have been greater than, less than, or equal to 10m/s? Neglect friction on both paths.
equal to
Select all of the following real life situations that approximate an elastic collision: 1) car runs into a brick wall 2) cue ball strikes another billiard ball 3) two oxygen molecules bump into each other, form O2, and travel in the direction the faster moving molecule was headed
example 2 only
Conservative forces
gravity, spring force
Center of mass
location of a system's average mass For an extended object-the point at which the object could be supported and be perfectly balanced; the force of gravity on the object acts as if it were applied at the center of mass
Isolated system
no net external force is exerted on the system OR assume short enough time that any external forces don't have time to significantly affect the system
When a car is coasting downhill, how are its potential and kinetic energies changing?
potential energy decreasing, kinetic energy increasing
What is recoil?
the backward momentum felt by an object or person exerting force on another object
Work-Kinetic Energy Theorem
the net work done by all the forces acting on an object is equal to the change in the object's kinetic energy Wnet=KEf-KE0
Power
the rate at which work is done P=W/t
Identify two properties that are expressed in units of joules.
work and kinetic energy
What is the equation for the impulse-momentum theorem?
Δ𝑝=𝐹netΔ𝑡 Yes, change in momentum is the product of average net external force and time during which the force was acting.
Which form of Newton's second law would you use to solve a problem in which mass varies?
𝐹net=Δ𝑝/Δ𝑡
What is the equation for Newton's second law of motion, in terms of mass, velocity and time, when the mass of the system is constant?
𝐹net=𝑚Δ𝑣/Δ𝑡 According to Newton's second law of motion, force is defined as the rate of change of momentum.
How can you state the law of conservation of momentum in equation form?
𝑝tot=𝑝′tot The momentum of the system is conserved. The conservation of linear momentum means that the initial momentum is equal to the final momentum of the system.