PHY 111 Test 2
REASONING STRATEGY Applying the Principle of Conservation of Linear Momentum
1.Decide which objects are included in the system. 2.Relative to the system that you have chosen, identify the internal forces and the external forces. 3.Verify that the system is isolated. In other words, verify that the sum of the external forces applied to the system is zero. Only if this sum is zero can the conservation principle be applied. If the sum of the average external forces is not zero, consider a different system for analysis. 4.Set the total final momentum of the isolated system equal to the total initial momentum. Remember that linear momentum is a vector. If necessary, apply the conservation principle separately to the various vector components.
A baseball pitcher throws a baseball and the batter hits it. During the hit, the baseball receives a greater impulse than the bat.
3rd Law forces are equal so impulses are also equal and they don't change Fx time or m x change in velocity
An airplane is flying horizontally with a constant momentum during a time interval Δt. (a) Is there a net impulse acting on the plane during this time? Use the impulse-momentum theorem to guide your thinking. (b) In the horizontal direction, both the thrust generated by the engines and air resistance act on the plane. Considering your answer to part (a), how is the impulse of the thrust related in magnitude and direction to the impulse of the force due to the air resistance? (a) No. (b) They're equal in magnitude and opposite in direction. (a) Yes. (b) They're equal in both magnitude and direction. (a) No. (b) They're equal in both magnitude and direction. (a) Yes. (b) They're equal in magnitude and opposite in direction.
A (a) No, because the momentum is constant. (b) The impulse of the thrust is equal in magnitude and opposite in direction to the impulse of the force due to air resistance. In this way, the net impulse is zero.
inelastic collision
A collision in which kinetic energy is not conserved. momentum is conserved
power
A measure of the rate of doing work or transferring energy
conservation
A particular measurable property of an isolated physical system does not change as the system evolves.
isolated system
A system that does not interact with its surroundings, that is, its total energy and mass stay constant
In 1971, Astronaut Alan B. Shepard Jr. hit 3 golf balls on the moon. The first two were 'duds', as it was hard to get a good swing (his suit weighed about 350 pounds on Earth, and is not very flexible), but the third went flying! If the gravity on Earth is 6 times that of the Moon, how many times further will a golf ball travel on the moon than one hit the same on Earth? Ignore wind resistance. A) 6 times C) 36 times E) same distance B) 1/6 as far D) 1/36 as far
A) 6 times ??
Why do most cars have anti-lock brakes, or why should you "pump" brakes in an older car if you wish to stop as quickly as possible? A) A "locked" tire invokes kinetic friction B) A "locked" tire invokes static friction
A) A "locked" tire invokes kinetic friction - which is the "weaker" friction
elastic collision
An encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total kinetic energy before the encounter. Elastic collisions occur only if there is no net conversion of kinetic energy into other forms. momentum is conserved
A satellite explodes in outer space, far from any other body, sending thousands of pieces in all directions. Is the linear momentum of the satellite before the explosion less than, equal to, or greater than the total linear momentum of all the pieces after the explosion? less than equal to greater than
B According to the principle of conservation of linear momentum, the linear momentum is conserved in this case because there are no external forces acting on the system.
Suppose you are standing on the edge of a dock and jump straight down. If you land on sand your stopping time is much shorter than if you land on water. Using the impulse-momentum theorem as a guide, determine which one of the following statements is correct. (a) In bringing you to a halt, the sand exerts a greater impulse on you than does the water. (b) In bringing you to a halt, the sand and the water exert the same impulse on you, but the sand exerts a greater average force. (c) In bringing you to a halt, the sand and the water exert the same impulse on you, but the sand exerts a smaller average force.
B Because the impulse is the same in both scenarios, the average force multiplied by the elapsed time will be the same. The sand will exert a larger average force since the elapsed time is shorter.
Imagine two balls colliding on a billiard table that is friction-free. Using the momentum-conservation principle as a guide, decide which statement is correct: (a) The total momentum of the system that contains only one of the two balls is the same before and after the collision. (b) The total momentum of the system that contains both of the two balls is the same before and after the collision.
B internal f12 and f21 cancel as well as weight force and normal force
(a) Can a single object have a kinetic energy and no momentum? (b) Can a group of two or more objects have a total kinetic energy that is not zero but a total momentum that is zero? (a) yes; (b) yes (a) yes; (b) no (a) no; (b) yes (a) no; (b) no
B no, yes (a) If an object has kinetic energy, then its has both mass and velocity and thus has momentum. (b) Kinetic energy is a scalar, but momentum is a vector. Even if the objects are moving, their total momenta could be zero because it's a vector. For example, two objects with the same mass and speed could be moving in opposite directions.
Although 80 gees are OK, brain trauma, such as concussion or worse, will result if the head suffers an acceleration of more than 100 gees for more than one millisecond. To help protect the brain, cerebrospinal fluid surrounds the tissue inside the scull. However, the density of CSF is greater than the density of grey and white matter. Assume a person is in a moving car that drives straight-on into a large tree. The head comes to a quick stop, either by hitting the steering wheel or an airbag. According to the first law, the area of the brain injury, which is where the brain tissue actually contacts the scull bone, is located where? A) in the front B) in the back C) on the sides
B) in the back ?? why
A net external force acts on a particle that is moving along a straight line. This net force is not zero. Which one of the following statements is correct? Entry field with correct answer The velocity, but not the kinetic energy, of the particle is changing. The kinetic energy, but not the velocity, of the particle is changing. Both the velocity and the kinetic energy of the particle are changing
Both Since the net force isn't zero, the kinetic energy will change. Since the kinetic energy changes, the speed will change, and speed is the magnitude of velocity, so the velocity will change as well.
Each planet has a different orbital speed around the sun. Rank the speeds of the first three planets in order of fastest to slowest. Spatially, the order is (M)ercury closest, then (V)enus, then the Earth (E) farthest. a) E, M, V b) E, V, M c) M, V, E d) V, E, M e) M, E, V
C GxMm/R^2 = mv^2/R this means R has a larger v
In Times Square in New York City, people celebrate on New Year's Eve. Some just stand around, but many move about randomly. Consider a group consisting of all of these people. Approximately, what is the total linear momentum of this group at any given instant? their total impulse their average speed multiplied by their total mass zero
C The average velocity of a group of objects moving randomly is zero. The total linear momentum is the average velocity multiplied by the total mass, so the total linear momentum is also zero.
Two objects have the same momentum. How do their velocities compare? They must have same directions and the same magnitudes. They must have the same magnitudes but they could have different directions. They must have the same directions but they could have different magnitudes. Their directions and the magnitudes could both be different.
C The velocities must have the same directions in order for the directions of their momenta to be the same. The velocities could have different magnitudes because their masses could be different.
If a football is kicked so that the force acts through the ball's center of gravity, the ball will: a) tumble end over end in the air. c) spin about its long axis in the air. b) not even get off of the ground. d) move without tumbling or spinning.
D No torque so no rotation
You are in a space ship and fire a cannonball into empty space. The amount of force necessary to keep the ball moving, in accordance with the laws of inertia, is: A) twice the force with which it was fired. B) the same amount of force with which it was fired. C) one-half the force with which it was fired. D) no force is required to keep it moving.
D no force is required to keep it moving.
An object slides along the surface of the earth and slows down because of kinetic friction. If the object alone is considered as the system, the kinetic frictional force must be identified as an external force that, according to Equation 7.4, decreases the momentum of the system. (a) If both the object and the earth are considered to be the system, is the force of kinetic friction still an external force? (b) Can the frictional force change the total linear momentum of the two-body system? (a) yes (b) yes (a) yes (b) no (a) no (b) yes (a) no (b) no
D No, No In this case, the frictional force is no longer external. Total momentum is conserved for the two bodies since the frictional forces are internal.
"Giddy-up horsey"! A horse pulls on a cart and the cart pulls back on the horse; do these two opposing forces cancel? If you are not careful with the logic, and the physics, you might come to the conclusion that no matter how hard the horse pulls, it can never move the cart. But you know a horse can pull a cart in "real life", so where is the flaw in this reasoning? The action and reaction forces do not cancel each other out because: A) the action and reaction forces do not cancel each other out because they are not equal in magnitude in this situation. B) they are equal in magnitude, but not precisely opposite in direction. C) they are equal in mag., opposite in direction, but do not act at the same time. D) they are not acting on the same body.
D) they are not acting on the same body.
You are standing in a small rowboat that has the same mass as you do. Considering the water as frictionless, if you walk forward 2 meters, the boat moves backwards two meters. With respect to the water, your net displacement is therefore zero. Tricky!
False The COM remains fixed by not the individual parts of the system ???
The change in momentum for any object in a closed system must be zero?
False True for the entire "system" but not one part of the system
A rocket is at rest on the launch pad. When the rocket is launched, its kinetic energy increases. Consider all of the forces acting on the rocket during the launch, and decide whether the following statement is true or false: The amount by which the kinetic energy of the rocket increases during the launch is equal to the work done by the force generated by the rocket's engine. True False
False there is more than just the engine's force acting on the rocket There are three forces acting on the rocket: the earth's gravity, air resistance and the force generated by the rocket's engine. The amount by which the kinetic energy of the rocket increases is equal to the net work done on the rocket.
Airbags protect people by decreasing the impulse suffered during crashes?
False Impulse= F x change in time Airbags reduce F by increasing delta T
The D = Vt equation is only valid if acceleration is a constant.
False only valid if A is zero (what kinematic formula is this??)
A perfectly elastic superball is dropped and bounces to the same height. Momentum is conserved for the following reason: The speed of the ball is the same just before and after the collision with the ground, and because its mass is constant, the value of m times v is the same.
False: momentum is not conserved force from the ground equals net external force (??? normal force doesn't cancel it out)
A bullet (mass = 15 grams, speed = 300 m/s) imbeds itself in a stationary block of wood (m=1500 grams). What is the final speed of the wood assuming no loss of material for either substance?
Fnet equls 0 so Pf=Pi M1V1i + M2V2i = M1V1f + M2V2f
The 15 balls on a pool table are put into the triangle, and the cue ball is used to "break". If the mass of each ball is the same 0.4 kg., and the initial speed of the cue ball is 6 m/s immediately before the collision, what is the total momentum of all 16 balls immediately after the collision? What, if anything, can you say about the total momentum 1 second after the break?
Fnet is 0 so Pf = Pi McueVcue (would've included balls in triangel but they're stationary so they would = 0 right??) = M1V1+...M16V16
Two ice skaters (zero friction) push off of each other while initially standing still. The 80 kg. skater is then moving north at 4.3 m/s. What is the 60 kg. skater doing?
Fnet is 0 so pi = pf at rest so initial is zero M1V1f/M2 = Vf2
A bullet (mass = 15 grams, speed = 300 m/s) imbeds itself in a stationary block of wood (m=1500 grams). What is the final speed of the wood assuming no loss of material for either substance?
Fnet is zero so Pi=Pf M1V1 + M2V2 = (M1+2) Vblob
A 10 kg. mass is placed on level ground with a static coefficient of friction of 0.7 and a kinetic coefficient of 0.5. How hard must a person push horizontally on the object to first get it to move.
Friction max (static) = mu*N = .7W = .7mg = 68.6 Newtons.
A horizontal spring is compressed a distance x = L. The spring is responsible, along with friction, for holding two objects in place against the walls without touching the floor. Find a relationship between mu-static and the spring constant k.
Fsp =k delta x = kL = Normal force in opposite direction Friction = mu x normal force = Weight force but in opposite direction = mg mu x k x L =mg
How fast would the Earth have to rotate in order for objects to just barely be touching the ground---so the normal force goes to zero?
GMemiss/ R^2 = mv^2/R why does the mass of iss cancel?? and why do we set it equal to mv^2/R
Derive the g = 9.8 number.
GMemyou/R^2 = mg ---> GMe/ Re^2
conservative forces
Gravitational force (Ch. 4) Elastic spring force (Ch. 10) Electric force
In which one or more of the following situations is the principle of conservation of mechanical energy obeyed? An object moves uphill with an increasing speed. An object moves uphill with a decreasing speed. An object moves uphill with a constant speed. An object moves downhill with an increasing speed. An object moves downhill with a decreasing speed. An object moves downhill with a constant speed.
If mechanical energy is conserved, then as kinetic energy increases, potential energy decreases and vice versa.
If you know the potential energy for only some of the forces, then the conservation of energy law in its most general form must be used
KEi+PEi+Wnc+OEi=KEf+PEf+OEf, where OE stands for all other energies.
If something always has a constant velocity, then it can still accelerate.
NO
While standing still, on a sloped surface, your weight is canceled by the normal force.
NO, not even in the same direction
An object thrown horizontally from a tall building hits sooner than if dropped.
NO--SAME—THE VERTICAL FALLING IS INDEPENDENT OF THE HORIZ VEL
If the net force on an object is zero, it will slow down and eventually stop.
NO—IF Fnet = 0, THE OBJECT WILL HAVE A CONSTANT VEL
A ball has a speed of 15 m/s. Only one external force acts on the ball. After this force acts, the speed of the ball is 7 m/s. Has the force done positive, zero, or negative work on the ball? positive zero negative
Negative work = change in KE the change in KE = KEf- KEi
Two identical automobiles have the same speed, one traveling east and one traveling west. Do these cars have the same momentum? Yes No
No Momentum is a vector.
Is momentum always conserved for any system?
No Only if Fnet = 0 on that system
A sailboat is moving at a constant velocity. Is work being done by a net external force acting on the boat? Yes. No.
No Since the boat's kinetic energy is constant, no work is being done on it.
Weight and Inertia both have units of Newtons.
No weight is in N mass is in Kg
Because of the t-squared, x = xo + vot + (1/2)at2 is valid if "a" changes in time
No- the equation is only valid if acceleration is constant
a pool ball movin 2.5 m/s has the exact same mass as a pool ball moving in the opposite direction at 9.8 m/s what is the final velocity
Po =m1v1+m2v2 Pf= the balls are the same mass so they will exchange speeds just need to find the direction change =-3
nonconservative work equals the change in mechanical energy true false
TRUE
A ball is dropped onto a hard surface. Immediately before the ball hits the surface it is traveling with a speed of . As it rebounds it travels with a reduced speed of . What is the impulse of the force that the surface exerts on the ball? Assume that the weight of the ball is negligible compared to the force that the surface exerts on the ball.
Taking up as the positive direction, the impulse-momentum theorem gives
potential energy
The energy an object has because of its position (in a gravitational or electric field) or its condition (as a stretched or compressed spring, as a chemical reactant, or by having rest mass)
principle of conservation of mechanical energy
The fact that the total mechanical energy is conserved when Wnc = 0 J
How could you get to the shore on a frictionless, iced-over, lake?
True Throw something in the opposite direction of intended motion
The Olympic bobsleds experience large "g forces" as they round corners at high speed. The speed of the sled is ~ 90 mph, or 40 m/s. If the radius of the curve is ~ 100 feet, or 32 meters, how many "gees" do the riders experience?
Use the v-squared over r formula to get 5 gees---this would be enough to force nearly anyone in this room to pass out and crash. This sport is no joke!!!
conservative force
Version 1 A force is conservative when the work it does on a moving object is independent of the path between the object's initial and final positions. Version 2 A force is conservative when it does no net work on an object moving around a closed path, starting and finishing at the same point.
A rope is tied to a tree limb. It is used by a swimmer who, starting from rest, swings down toward the water below, as in Figure 6.17. Only two forces act on him during his descent, the nonconservative force , which is due to the tension in the rope, and his weight, which is due to the conservative gravitational force. There is no air resistance. His initial height h0 and final height hf are known. Can we use the principle of conservation of mechanical energy to find his speed vf at the point where he lets go of the rope, even though a nonconservative external force is present? (a) Yes. (b) No.
When nonconservative forces are perpendicular to the motion, we can still use the principle of conservation of mechanical energy, because such "perpendicular" forces do no work
If something always has a constant speed, then it can still accelerate.
YES
The Moon travels at a constant speed, but is accelerating in its orbit around the Earth.
YES
The Vf2 = Vi2 + 2a(∆R) equation is only valid if acceleration is a constant.
YES
It is possible to accelerate towards a certain point in space but never actually get there.
YES- for instance the center of a circle
When a baseball is hit by a bat, it is possible for the ball to accelerate at several hundred 'gees'.
Yes
On a distant asteroid, a large catapult is used to throw chunks of stone into space. Could such a device be used as a propulsion system to move the asteroid closer to the earth? Yes No
Yes Question 3 The asteroid will move in the direction opposite the direction in which the chunks of stone were thrown.
In 2010, the U.S. national debt reached ~ 12.5 trillion dollars, where a trillion is a thousand billion. If payments were made at the rate of $1000 per second, it would take how long to pay off the debt—assuming no interest is charged. A) about 396 years B) about 396 months C) about 396 days
about 396 years
Figure 6.9 illustrates a satellite moving about the earth in a circular orbit and in an elliptical orbit. The only external force that acts on the satellite is the gravitational force. In which orbit does the kinetic energy of the satellite change, (a) the circular orbit or (b) the elliptical orbit?
b elliptical in a circle F and S are perpendicular this means theta would be 90 and cos (90) =0 and there is no work done in an elliptical orbit F and S are not perpendicular so work is done
Newton actually stated his second law of motion in terms of momentum
change in momentum of a system over the time it changes
non-conservative forces
friction air resistance normal force tension
How far away are the following satellites: Spy Agency, ISS, Geo-Sync. Various "spy" sats can be optical or radar. The advanced radar ones are code-named "Topaz", and there are 3 new ones now and 2 more to come soon. The optical sats have run into lots of tech problems and $$ overruns, but spys go as low as ~ 100 miles. So, the answers are: as low as ~ 100 miles for spy, about 220 miles for ISS, and...?? for the geo-sync sats?
how do we know to use v = root GMe/R and 2piR=VT v62 = 4pi^2R^2/Tperiod ^2 and how do we know the period that equation isn't given
Frictional force
is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other.
The total mechanical energy
is the sum of the kinetic and potential energies.
velocity of a center of mass
m1v1 + m2v2 (m1+m2) doesn't change if linear momentum is conserved
impulse is the change in....
momentum
The average power developed by a force of magnitude F, moving an object with an average speed, is
p = f v
A penguin walks forwards and backwards on a boat floating frictionless in water. The COM does..?
remains motionless because Fnet System equals zero how do we know what is in the system?? is it because N and W cancel and no friction and velocity is canceled because forward and backward?
In a simulation on earth, an astronaut in his space suit climbs up a vertical ladder. On the moon, the same astronaut makes the exact same climb. Which one of the following statements describes how the gravitational potential energy of the astronaut changes during the climb? It changes by a greater amount on the earth. It changes by a greater amount on the moon. The change is the same in both cases.
t changes by a greater amount on the earth. Since the magnitude of the acceleration due to gravity is greater on the earth, then the gravitational potential energy will change by a greater amount there
The work-energy theorem
the work done by all forces acting on a particle equals the change in the particle's kinetic energy
The change in both the kinetic and the potential energy is always the final value minus the initial value: ΔKE = KEf − KE0 and ΔPE = PEf − PE0 true false
true
The concept of potential energy is not defined for a nonconservative force. true false
true
How fast would the Earth have to rotate in order for objects to just barely be touching the ground---so the normal force goes to zero?
w force is the only force mv^2/R = mg v= ^2 root Rgravity why do we set it equal to mv^2/R