PHYS 107 test 2
A 1-kg glider and a 3-kg glider both slide toward each other at 2 m/s on an air track. They collide and stick. The combined mass moves at
1m/s m1v1 + m2v2 = (m1 + m2)V1+2 inelastic 1x-2 + 3x2=4vf -2 + 6 = 4 4=4
If you need to tighten a bolt with 80 Nm of torque using a wrench with a handle that is 25 cm from the axis of the bolt, how much force do you need to apply when turning the wrench?
320 N
When you whirl a can at the end of a string in a circular path, what is the direction of the force you exert on the can?
Toward the center of the circle
centripetal force
a force that acts on a body moving in a circular path and is directed toward the center around which the body is moving. F=mv^2/r
A simple lever, properly arranged, is capable of multiplying work input.
always false
centrifugal force
an apparent force that acts outward on a body moving around a center, arising from the body's inertia.
If a trapeze artist rotates once each second while sailing through the air, and contracts to reduce her rotational inertia to one third of what it was, how many rotations per second will result?
angular momentum is conserved (Li = Lf) L = Iw L = (1/3 * I)(3 w) 3 rotations per second
Acrobat Bart at the circus drops vertically onto the end of a see -saw, with his partner Art equidistant from the fulcrum at the other end. Art is propelled straight upward a distance twice that of Bartʹs dropping distance. Neglecting inefficiencies we see
art has half the mass of bart
center of mass
average position of the mass of an object. The CM moves as if all the external forces acted at this point
Your pet hamster sits on a spinning record player. If the angular speed of the record player doubles and he moves to a point twice as far from the center, then his linear speed (assuming he doesnʹt fly o the record player and onto the floor, causing PETA and SPCA to come after you)
doubles
torque
force x lever arm distance tends to produce a change in rotation
impulse
force x time; change in momentum
distinguish between force and impulse
force: any push or pull impulse: force X time
Which has greater kinetic energy, a car traveling at 30 km/hr or a car of half the mass traveling at 60 km/hr?
the 60 km/hr car
energy
the ability to do work
kinetic energy
the energy an object has due to its motion 1/2 mass x speed squared KE=1/2mv^2
Two billiard balls of the same mass roll straight toward each other. The first has a velocity of +5 m/s and the second has a velocity of -3 m/s. After colliding, the first ball has a velocity of
-3m/s or 2m/s
When the speed of a moving car is doubled, how much more kinetic energy does it have?
4 times more
A jack system will increase the potential energy of a heavy load by 400 J and generate 600 J of heat with a work input of 1000 J. The efficiency of the jack system is
40%
To do 10 J of work pushing a crate using 2 N of force, you will need to push the crate
5 m
How long will it take to stop a 1500 kg car moving at 20 m/s with a braking force of 6000 N?
5 seconds M=mv M= 30,000kgm/s 30,000/6,000=5s
A 2-kg mass is held 4 m above the ground. What is the approximate potential energy of the mass with respect to the ground?
80 J
elastic collision
A collision in which colliding objects rebound without lasting deformation or the generation of heat.
inelastic collision
A collision in which the colliding objects become distorted, generate heat, and possibly stick together.
machine
A device, such as a lever or pulley, that increases (or decreases) a force or simply changes the direction of a force.
Discuss why one should even bother to use a machine if it cannot multiply work input to achieve greater work output. What, then, is the use of a machine?
A machine can multiply force or multiply distance, both of which can be of value
Can a machine multiply input force? Input distance? Input energy? (If your three answers are the same, seek help; the last question is especially important.
A machine can multiply input force or input distance, but NEVER input energy.
To tighten a bolt you push with a force of 80N at the end of a wrench handle that is 0.25m from the axis of the bolt. A) What torque are you exerting? B) If you move your hand inward to be only 0.10m from the bolt, to achieve the same torque show that you should exert 200N of force. C) Do your answers depend on the direction of your push relative to the direction of the wrench handle?
A) T=lever arm x force T=(0.25M)(80n) T=20 N/M B) (0.10)(200N) T= 20 N/M C) Yes, the force must be applied perpendicular to the wrench handle
in terms of impulse and momentum, why do airbags in cars reduce the risk of injury in accidents?
Airbags cause momentum to change over a greater time which slows down and reduces the force
Distinguish between linear momentum and angular momentum.
Angular momentum depends on the distribution of mass, whereas linear momentum depends on the total mass.
Which, if either, has greater momentum: a 1kg ball moving at 2m/s or a 2kg ball moving at 1m/s? Which has greater KE?
Both have the same momentum, but the faster 1-kg one has the greater KE.
Consider the swinging balls apparatus. If two balls are lifted and released, momentum is conserved as two balls pop out the other side with the same speed as the released balls at impact. But momentum would also conserved if one ball popped out at twice the speed. Discuss why this never happens.
But now look at this situation in accordance with the conservation of energy (½ m v2) If only 1 ball pops out with twice the velocity Energy before = ½ m v2 + ½ m v2 = m v2 Energy after = ½ (m) (2 v)2= ½ (m) (4 v2) = 2 m v2 These energies are not equal and, therefore, the law of conservation of energy is not obeyed! But, since 2 balls actually popped out Energy before = ½ m v2 + ½ m v2 = m v2 Energy after = ½ m v2 + ½ m v2 = m v2 These energies are equal and, therefore, both laws of conservation are obeyed
What is the efficiency of a machine that miraculously converts all the input energy to useful output energy?
Efficiency would be 100%.
Compared with a car moving at some original speed, how much work must the brakes of a car supply to stop a car that is moving twice as fast? How will the stopping distance compare?
Four times as much work; 4 times as much stopping distance
If a skater who is spinning pulls her arms in so as to reduce her rotational inertia by half, by how much will her angular momentum change? By how much will her rate of spin change?
Her angular momentum does not change. Her spin rate doubles.
If a golf ball and a Ping-Pong ball both move with the same kinetic energy, can you say which has the greater speed? Explain in terms of the definition of KE. Similarly, in a gaseous mixture of heavy molecules and light molecules with the same average KE, can you say which have the greater speed?
If KEs are the same but masses differ, then the ball with smaller mass has the greater speed.
Light consists of tiny "corpuscles" called photons that possess momentum. This can be demonstrated with a radiometer, shown in the sketch. Metal vanes painted black on one side and white on the other are free to rotate about the point of a needle mounted in a vacuum. When photons are incident on the black surface, they are absorbed; when photons are incident upon the white surface, they are reflected. Upon which surface is the impulse of incident light greater, and which way will the vanes rotate? (They rotate in the opposite direction in more common radiometers where air is present in the glass chamber; your instructor may tell you why.) Explain.
If no air is present the impulse on the white (or reflecting) surface will be greater, although not by as much as at first sight. The reason is that on reflection from the white surface the momentum of each photon changes sign, so that if p is the momentum when incident, -p is the momentum when reflected. The change in momentum is thus p-(-p)=2p per photon.
The occupant inside a future rotating space habitat feels that she is being pulled by artificial gravity against the outer wall of the habitat (which becomes the "floor"). Explain what is going on in terms of Newton's laws and centripetal force.
If the floor were not present, she would want to continue to move tangent and fly off of the habitat, as stated by Newton's first law. However, at the correct speed, the floor that is stopping her simulates the feeling of gravity as it keeps her in the habitat. The force acting on her and the habitat, however, is still center-seeking.
Why is it important to secure cabinets to the floor, especially cabinets with heavy loads in top drawers?
If you pull open the upper drawers of a fully-loaded file cabinet that isn't secured to the floor, the CG of the cabinet can easily be shifted beyond the support base of the cabinet, causing it to topple over.
An apple hanging from a limb has PE because of its height. If it falls, what becomes of this energy just before it hits the ground? When it hits the ground?
Immediately before hitting the ground its initial PE becomes KE. When it hits the ground its energy becomes thermal energy.
What is meant by the "lever arm" of a torque?
It is the perpendicular distance from the rotational axis to the line along which the force acts.
Calculate the KE of an 84kg scooter moving at 10 m/s. KE = ½mv²
KE = ½ mv2 = ½(84 kg)(10 m/s)2 = 4200 kg(m/s)2 = 4200 J
mechanical energy
Kinetic or potential energy associated with the motion or position of an object
Joanne drives her car with a mass of 1000kg, moves at 20 m/s. What braking force is needed to bring the car to a halt in 10 seconds?
M=mv -- M=(1000kg)(20m/s)= 20000 kg*m/s 20000 kgm/s / 10s = 2000 N it would need a breaking force of 2000 N to stop the car in 10s
Is the net torque changed when a partner on a seesaw stands or hangs from her end instead of sitting? (Does the weight or the lever arm change?)
No because the distance that the force is applied on is still the same.
If the string that holds a whirling can in its circular path breaks, what kind of force causes it to move in a straight- line path: centripetal, centrifugal, or no force? What law of physics supports your answer?
No force; Newton's first law
If two objects have equal KE, do they necessarily have the same momentum? Defend
Not at all. For two objects of the same KE, the one of greater mass has greater momentum. (The mathematical relationship is p2 = 2m x KE.)
Show that about 786W of power is expended when a 500N barbell is lifted 2.2m above the floor in 1.4s. P= W/t
P = W/t = Fd/t = (500 N)(2.2 m)/(1.4 s) = 786 W.
gravitational potential energy
Potential energy that depends on the height of an object weight x height PE=mgh
angular momentum
Product of rotational inertia and rotational velocity about a particular axis angular momentum = mvr
Why is it easier to stop a lightly loaded truck than a heavier one that has equal speed?
Stopping a lightly loaded truck of the same speed is easier because it has less KE and will therefore require less work to stop. (An answer in terms of impulse and momentum is also acceptable.)
On a rotating turntable, how do tangential speed and rotational speed vary with distance from the center?
Tangential speed increases with distance. Rotational speed is constant.
At what point in its motion is the KE of a pendulum bob at a maximum? At what point is its PE at a maximum? When its KE is at half its maximum value, how much PE does it have relative to its PE at the center of the swing?
The KE of a pendulum bob is maximum where it moves fastest, at the lowest point; PE is maximum at the uppermost points. When the pendulum bob swings by the point that marks half its maximum height, it has half its maximum KE, and its PE is halfway between its minimum and maximum values. If we define PE = 0 at the bottom of the swing, the place where KE is half its maximum value is also the place where PE is half its maximum value, and KE = PE at this point. (By energy conservation: Total energy = KE + PE.)
center of gravity
The average position of weight or the single point associated with an object where the force of gravity can be considered to act.
Which will have the greater acceleration rolling down an incline: a bowling ball or a volleyball? Defend your answer.
The bowling ball because it has less rotational inertia per unit mass.
In terms of center of gravity, support base, and torque, why can you not stand with heels back to a wall and then bend over to touch your toes and return to stand up position?
The center of gravity moves when you move forward so the center of gravity isn't in line with the support base.
Where is the center of mass of a baseball? Where is its center of gravity? Where are these centers for a baseball bat?
The center of mass and the center of gravity are both at the center of the spherical ball. For a bat, it it toward the thicker end
Inertia depends on mass; rotational inertia depends on mass and something else. What?
The distribution of mass about the axis of rotation
A force of 50N is applied to the end of a lever, which is moved a certain distance. If the other end of the lever moves one-third as far, how much force can it exert?
The end moving 1/3 as far can exert 3 times the input force, 150 N.
Efficiency
The percentage of the input work that is converted to output work Efficiency = useful energy output / total energy input
Does the KE of a car change more when it goes from 10 to 20 km/h or when it goes from 20 to 30 km/h?
The question can be restated; Is (30 squared minus 20 squared) greater or less than (20 squared - 10 squared)? Se see that (30 squared - 20 squared) = (900 - 400) = 50, which is considerably greater than (20 squared - 20 squared) = (400 - 100) = 300. j So KE changes more for a given change in velocity at the higher speed.
You sit at the middle of a large turntable at an amusement park as it is set spinning and then allowed to spin freely. When you crawl toward the edge of the turntable, does the rate of the rotation increase, decrease, or remain unchanged? What physics principle supports your answer?
The rate of rotation decreases as you crawl out to the rim while rotational inertia increases is accordance with the conservation of angular momentum.
Why does a typical small helicopter with a single main rotor have a second small rotor on its tail? Describe the consequence if the small rotor fails in flight.
The small rotor exerts a force at the end of a long lever arm. This provides a "rotational force" on the helicopter to oppose or counteract the "rotational force" supplied by the main rotor. Consider a helicopter initially at rest. As the main rotor starts and gains angular momentum, the body must have a "rotational force" on it or it will start rotating in the opposite direction so that it has angular momentum in the other direction. The small tail rotor supplies a "rotational force" so the body does not rotate.
work-energy theorem
The work done on an object equals the change in kinetic energy of the object Fd=1/2mv^2
In the absence of air resistance, a ball thrown vertically upward with a certain initial KE will return to its original level with the same KE. When air resistance is a factor affecting the ball, will it return to its orginial level with the same, less, or more KE? Does your answer contradict the law of energy conservation?
When air resistance is a factor, the ball will return with less speed. It therefore will have less KE. You can see this directly from the fact that the ball loses mechanical energy to the air molecules its encounters, so when it returns to its starting point and to its orginial PE, it will have less KE. This does not contradict energy conservation, for energy is transformed, not destroyed.
conservation of angular momentum
When no external torque acts on an object or a system of objects, no change of angular momentum can occur. Hence, the angular momentum before an event involving only internal torques or no torques is equal to the angular momentum after the event.
Railroad cars are loosely coupled so that there is a noticeable time delay from the time the first car is moved until the last cars are moved from rest by the locomotive. Discuss the advisability of this loose coupling and slack between cars from the point of view of impulse and momentum.
Without this slack, a locomotive might simply sit still and spin its wheels. The loose coupling enables a longer time for the entire train to gain momentum, requiring less force of the locomotive wheels against the track. In this way, the overall required impulse is broken into a series of smaller impulses. (This loose coupling can be very important for braking as well).
Two people who weigh the same climb a flight of stairs. The first person climbs the stairs in 30s and the second person climbs them in 40s. Which person does more work? Which uses more power?
Work done by each is the same, for they reach the same height. The one who climbs in 30 s uses more power because work is done in a shorter time.
Does the international space station have gravitational PE? KE? Explain
Yes to both, relative to Earth, because work was done to lift it in Earth's gravitational field and to impart speed to it.
lever
a simple machine that consists of a bar that pivots at a fixed point called a fulcrum
Exactly what is it that enables an object to do work?
energy
to impart the greatest momentum to an object, you should
exert the largest force possible over the longest period of time
work
force x distance moved in direction of force (Nm = J)
When a car is braked to a stop, its kinetic energy is transformed to
heat
An upright broom is easier to balance when the heavier end is
highest, farthest from your hand.
Why is it advantageous for a boxer to ride with the punch? Why should he avoid moving into an oncoming punch?
if a boxer rides with the punch, he extends the time and diminished the force. if there is less time, the force is greater.
A longer cannon barrel is advantageous because it increases
impulse delivered to the ball by allowing the force to be applied for a longer time.
impulse-momentum relationship
impulse is equal to the change in the momentum of an object that the impulse acts upon. Ft= Δmv
law of conservation of momentum
in the absence of an external force, the momentum of a system remains unchanged. hence, the momentum before an event involving only internal forced is equal to the momentum after. mv before= mv after
In which is momentum conserved: an elastic collision or an inelastic collision?
it is conserved in both elastic and inelastic collisions
A car is raised a certain distance in a service station lift and therefore has potential energy relative to the floor. If it were raised twice as high, how much more potential energy would it have?
it would have twice the PE because the distance is 2x as much
Momentum
mass x velocity
A heavy truck and a light truck roll down a hill. Neglecting friction, at the bottom of the hill, the heavy truck will have greater
momentum
A heavy truck and a light truck roll down a hill. Neglecting friction, at the bottom of the hill, the light truck will have less
momentum
When you are in the front passenger seat of a car turning to the left, you may find yourself pressed against the right-side door. Why do you press against the door? Why does the door press on you? Does your explanation involve a centrifugal force, or Newton's laws?
newtons first law - you tend to move in straight line but are intercepted by the door newtons third law - you press against the door because the door is pressing against you the push by the door provides the centripetal force that keeps you moving in a curved path no centrifug
When a cannonball is fired, momentum is conserved for the system cannon + cannonball. would momentum be conserved for a system if momentum were not a vector quantity? explain
no, momentum would not be conserved if it was not a vector quantity. If no direction was known, they would not cancel out - conserving the momentum
Doing twice the usual work on an object in four times the usual time requires
one half the usual power
A ring, a disk, and a solid sphere begin rolling down a hill together. The one to reach the bottom last is the
ring
Which requires the most amount of work by the brakes of a car?
slowing down from 100 km/h to 70 km/h
potential energy
stored energy that results from the position or shape of an object
Law of Conservation of Energy
the law that states that energy cannot be created or destroyed but can be transformed from one form to another. The total amount of energy never changes
rotational speed
the number of rotations or revolutions per unit of time RPM or radians/s
linear momentum
the product of the mass and velocity of an object
power
the rate at which work is done work done/time interval J/s = watt (W)
rotational inertia
the resistance of an object to changes in its rotational motion
tangential speed
the speed of something moving along a circular path v ~ radial distance x rotational speed
Equilibrium
the state of an object in which it is not acted upon by a net force or a net torque
conservation of energy
the work output of any machine cannot exceed the work input work input=work output
Here are the familiar pair of carts connected by a spring. (m--2m) What are the relative speeds of the carts when the spring is released? M 2M
when the carts are released, the cart with 2m has 1/2 the speed of m; 2m(v/2)=mv
a force sets an object in motion. when the force is multiplied by the time of its application we call the quantity impulse which changes the momentum of that object. what do we call the quantity force x distance?
work is Fd
