Physics 1 Exam 3
A 2.0-kg ball moving eastward at 3.0 m/s suddenly collides with and sticks to a 4.0-kg ball moving northward at 2.0 m/s. What is the magnitude of the momentum of this system just after the collision?
10 kg⋅m/s
A tiger is running in a straight line. If we double both the mass and speed of the tiger, the magnitude of its momentum will increase by what factor?
4
If you want to double the momentum of a gas molecule, by what factor must you increase its kinetic energy?
4
A 60-kg woman stands on the very end of a uniform board, of length l, which is supported one-quarter of the way from one end and is balanced. What is the mass of the board?
60 kg
Consider a force F = 80 N applied to a beam as shown in Fig. 8-37. The length of the beam is l = 5.0 m, and θ = 36.9°, so that x = 3.0 m and y = 4.0 m. Of the following expressions, which ones give the correct torque produced by the force around point P?
80N × 3.0m
Two uniform solid balls, one of radius R and mass M, the other of radius 2R and mass 8M, roll down a high incline. They start together from rest at the top of the incline. Which one will reach the bottom of the incline first?
Both reach the bottom at the same time.
Impulse Formula
FΔt
A spinning ice skater on extremely smooth ice is able to control the rate at which she rotates by pulling in her arms. Which of the following statements are true about the skater during this process?
Her angular momentum remains constan
Two children, Ahmed and Jacques, ride on a merry-go-round. Ahmed is at a greater distance from the axis of rotation than Jacques. Which of the following are true statements?
Jacques and Ahmed have the same angular speed
Torque
Moment of force about an axis the angular acceleration of an object is directly proportional to the net applied torque
A very light ping-pong ball moving east at a speed of 4 m/s collides with a very heavy stationary bowling ball. The Ping-Pong ball bounces back to the west, and the bowling ball moves very slowly to the east. Which object experiences the greater magnitude impulse during the collision?
Neither; both experienced the same magnitude impulse.
When is the angular momentum of a system constant?
Only when no net external torque acts on the system
Momentum (p)
Product of its mass and its velocity The unit of momentum: mass times velocity (m x s) direction of momentum is the velocity and magnitude of momentum Units: kg times m/s
A bowling ball hangs from a 1.0-m-long cord, Fig. 7-30: (i) A 200-gram putty ball moving 5.0 m/s hits the bowling ball and sticks to it, causing the bowling ball to swing up; (ii) a 200-gram rubber ball moving 5.0 m/s hits the bowling ball and bounces straight back at nearly 5.0 m/s, causing the bowling ball to swing up. Describe what happens.
The ball swings up farther in (ii) than in (i).
A baseball is pitched horizontally toward home plate with a velocity of 110 km/h. In which of the following scenarios does the baseball have the largest change in momentum?
The baseball is hit straight back to the pitcher at a speed of 110 km/h.
A very elastic rubber ball is dropped from a certain height and hits the floor with a downward speed v. Since it is so elastic, the ball bounces back with the same speed v going upward. Which of the following statements about the bounce are correct?
The magnitude of the ball's momentum was the same just before and just after the bounce.
A 5-kg ball collides inelastically head-on with a 10-kg ball, which is initially stationary. Which of the following statements is true?
The magnitude of the change of velocity the 5-kg ball experiences is greater than that of the 10-kg ball.
A small car meshes with a large truck in a head-on collision. Which of the following statements concerning the momentum during the collision are correct?
The momentum of the car-truck system is conserved, but the momentum of each one separately is not conserved.
A rocket explodes into two fragments, one 25 times heavier than the other. The magnitude of the momentum change of the lighter fragment is
The same as the momentum change of the heavier fragment.
A small car meshes with a large truck in a head-on collision. Which of the following statements concerning the magnitude of the average force during the collision is correct?
The small car and the truck experience the same average force.
A small car meshes with a large truck in a head-on collision. Which of the following statements concerning the magnitude of the momentum change during the collision is correct?
The small car and the truck experience the same magnitude momentum change.
Law of Conservation of Momentum
The total momentum of an isolated system of abject remains constant Follows from Newtons 2nd Law Useful when dealing with simple problems of colliding objects & certain explosions
Two wheels having the same radius and mass rotate at the same angular velocity (Fig. 8-38). One wheel is made with spokes so nearly all the mass is at the rim. The other is a solid disk. How do their rotational kinetic energies compare?
The wheel with spokes has about twice the ke.
A truck going 15 km/h has a head-on collision with a small car going 30 km/h. Which statement best describes the situation?
They both have the same change in magnitude of momentum because momentum is conserved.
A small car and a heavy pickup truck are both out of gas. The truck has twice the mass of the car. After you push both the car and the truck over the same distance with the same force, what can you say about the momentum and kinetic energy of the car and the truck? Ignore friction.
They have the same kinetic energy, but the truck has more momentum than the car.
A small car and a heavy pickup truck are both out of gas. The truck has twice the mass of the car. After you push both the car and the truck for the same amount of time with the same force, what can you say about the momentum and kinetic energy of the car and the truck? Ignore friction.
They have the same momentum, but the car has more kinetic energy than the truck.
An astronaut is a short distance away from her space station without a tether rope. She has a large wrench. What should she do with the wrench to move toward the space station?
Throw it directly away from the space station.
A car is traveling along a freeway at 65 mph. What is the linear speed at the top, middle, and bottom of the tire?
Top: 130 mph Middle: 0 mph Bottom: 65 mph
Consider a solid uniform sphere of radius R and mass M rolling without slipping. Which form of its kinetic energy is larger, translational or rotational?
Translational kinetic energy is larger.
Inelastic Collision
When KE is not conserved When 2 objects stick together after collision The KE lost is changed into other forms of energy (thermal) so that the total energy is conserved V121 < v12
If the answer to your calculation has units of kg⋅m2/s, what type of quantity could it be?
angular momentum
Consider a uniform hoop of radius R and mass M rolling without slipping. Which is larger, its translational kinetic energy or its rotational kinetic energy?
both are equal
When you apply the torque equation Στ = 0 to an object in equilibrium, the axis about which torques are calculated
can be located anywhere
A small boat coasts at constant speed under a bridge. A heavy sack of sand is dropped from the bridge onto the boat. The speed of the boat
decreases
You are standing on a skateboard, initially at rest. A friend throws a very heavy ball towards you. You have two choices about what to do with the ball: either catch the ball or deflect it back toward your friend with the same speed as it was originally thrown. Which choice should you make in order to maximize your speed on the skateboard?
deflect the ball back
As you are leaving a building, the door opens outward. If the hinges on the door are on your right, what is the direction of the angular velocity of the door as you open it?
down
In a game of pool, the white cue ball hits the #5 ball and stops, while the #5 ball moves away with the same velocity as the cue ball had originally. Both balls have the same mass. This type of collision is
elastic
Identical forces act for the same length of time on two different objects. The magnitude of the change in momentum of the lighter object is
exactly equal to the magnitude of the change in momentum of the larger mass.
In an inelastic collision involving an isolated system, the final total momentum is
exactly the same as the initial momentum.
There must be equal amounts of mass on both sides of the center of mass (or center of gravity) of a system.
false
A railroad car collides with and sticks to an identical railroad car that is initially at rest. After the collision, the kinetic energy of the system
half as much as before
Bonnie sits on the outer rim of a merry-go-round, and Jill sits midway between the center and the rim. The merry-go-round makes one complete revolution every 2 seconds. Jill's linear velocity is:
half of bonnies
A person sits on a freely spinning lab stool that has no friction in its axle. When this person extends her arms,
her moment of inertia increases and her angular speed decreases.
A ballet dancer is spinning in the middle of a horizontal frictionless stage. Which of the following things can he not change by moving parts of his body or his whole body?
his angular momentum
The momentum of an isolated system is conserved
in both elastic and inelastic collisions
If there were a great migration of people toward the Earth's equator, the length of the day would
increase because of conservation of angular momentum.
A small mass m on a string is rotating without friction in a circle. The string is shortened by pulling it through the axis of rotation without any external torque. What happens to the angular velocity of the object?
increases
A small mass m on a string is rotating without friction in a circle. The string is shortened by pulling it through the axis of rotation without any external torque. What happens to the tangential velocity of the object?
increases
If the angular velocity of a rotating object changes
it has tangential acceleration
Quantity units of momentum
kg*m/s N*s
Units of impulse
kg*m/s N*s
A solid sphere and a solid cylinder, both uniform and of the same mass and radius, roll without slipping at the same forward speed. It is correct to say that the total kinetic energy of the solid sphere is
less than the total kinetic energy of the cylinder.
momentum before = momentum after
m1 • v1 + m2 • v2 = m1 • v1' + m2 • v2'
A railroad tank car contains milk and rolls at a constant speed along a level track. The milk begins to leak out the bottom. The car then
maintain constant speed
If a quantity you calculated had units of kg⋅m/s, what type of quantity could it be?
momentum and impulse
A uniform beam is hinged at one end and held in a horizontal position by a cable. The tension in the cable
must be at least half the weight of the beam, no matter what the angle of the cable.
Suppose a uniform solid sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The linear velocity of the sphere at the bottom of the incline depends on
neither the mass nor the radius of the sphere.
Two identical billiard balls traveling at the same speed have a head-on collision and rebound. If the balls had twice the mass, but maintained the same size and speed, how would the rebound be different?
no difference
An egg falls from a bird's nest in a tree and feels no effects due to the air. As it falls,
only its mechanical energy is conserved.
The space shuttle, in circular orbit around the Earth, collides with a small asteroid which ends up in the shuttle's storage bay. For this collision,
only momentum is conserved.
On a horizontal frictionless air table, a puck runs into an ideal horizontal spring that is fastened to the table. The puck compresses the spring by 15 cm before coming to rest. During the compression process, which quantities are conserved?
only the mechanical energy (kinetic plus potential) of the puck
Momentum Formula
p=mv
Center of Gravity (CG)
point where the gravitational force can be considered to act CM = CG
If the answer to your calculation has units of kg⋅m2/s2 , what type of quantity could it be?
rational kinetic energy
In a collision between two unequal masses, which mass receives a greater magnitude impulse?
receive equal impulse
Two children are balanced on opposite sides of a seesaw. If one child leans inward toward the pivot point, her side will
rise
If you used 1000 J of energy to throw a ball, it would travel faster if you threw the ball (ignoring air resistance)
so that it wasn't rotating
A small uniform disk and a small uniform sphere are released simultaneously at the top of a high inclined plane, and they roll down without slipping. Which one will reach the bottom first?
sphere
A solid sphere, solid cylinder, and a hollow pipe all have equal masses and radii. If the three of them are released simultaneously at the top of an inclined plane and do not slip, which one will reach the bottom first?
sphere
A disk, a hoop, and a solid sphere are released at the same time at the top of an inclined plane. They are all uniform and roll without slipping. In what order do they reach the bottom?
sphere, disk, hoop
If you want to double the kinetic energy of a gas molecule, by what factor must you increase its momentum?
square root of 2
Two friends are standing on opposite ends of a canoe that is initially at rest with respect to a frictionless lake. The person in the front throws a very massive ball toward the back, and the person in the back catches it. After the ball is caught, the canoe is
stationary
A firecracker explodes in midair and breaks up into many fragments. Which of the following statements are true regarding conditions immediately before and immediately after the explosion: I. The total momentum of the fragments is equal to the original momentum of the firecracker. II. The total kinetic energy of the fragments is equal to the original kinetic energy of the firecracker.
statment I
Suppose you are sitting on a rotating stool holding a 2-kg mass in each outstretched hand. If you suddenly drop the masses, your angular velocity will
stay the same
A rubber ball and a lump of clay have equal mass. They are thrown with equal speed against a wall. The ball bounces back with nearly the same speed with which it hit. The clay sticks to the wall. Which one of these objects experiences the greater momentum change?
the ball
A disk and a hoop of the same mass and radius are released at the same time at the top of an inclined plane. If both are uniform, which one reaches the bottom of the incline first if there is no slipping?
the disk
Two equal-magnitude forces are applied to a door at the doorknob. The first force is applied perpendicular to the door, and the second force is applied at 30° to the plane of the door. Which force exerts the greater torque about the door hinge?
the first force (applied perpendicular to the door)
Two forces produce equal torques on a door about the door hinge. The first force is applied at the midpoint of the door; the second force is applied at the doorknob. Both forces are applied perpendicular to the door. Which force has a greater magnitude?
the first force (at the midpoint)
A heavy ball suspended by a cable is pulled to the side by a horizontal force. If angle θ is small, the magnitude of the force F can be less than the weight of the ball because:
the force is equal to only the x component of the tension in the cable.
Consider two less-than-desirable options. In the first you are driving 30 mph and crash head-on into an identical car also going 30 mph. In the second option you are driving 30 mph and crash head-on into a stationary brick wall. In neither case does your car bounce back from the thing it hits, and the collision time is the same in both cases. Which of these two situations would result in the greater impact force on your car?
the force would be the same in both cases
A golf ball and an equal-mass bean bag are dropped from the same height and hit the ground. The bean bag stays on the ground while the golf ball rebounds. Which experiences the greater impulse from the ground?
the golf ball
Two objects of different mass have equal, non-zero kinetic energies. Which object has the greater magnitude momentum?
the heavier object
Two spheres have the same radius and equal mass. One sphere is solid, and the other is hollow and made of a denser material. Which one has the bigger moment of inertia about an axis through its center?
the hollow one
A small solid sphere and a small thin hoop are rolling along a horizontal surface with the same translational speed when they encounter a 20° rising slope. If these two objects roll up the slope without slipping, which will rise farther up the slope?
the hoop
A rubber ball bounces off of a wall with an initial speed v and reverses its direction so its speed is v right after the bounce. As a result of this bounce, which of the following quantities of the ball are conserved?
the kinetic energy of the ball
Two objects of different masses have momentum of equal, non-zero magnitude. Which object has more kinetic energy?
the lighter object
A merry-go-round spins freely when Diego moves quickly to the center along a radius of the merry-go-round. As he does this, it is true to say that
the moment of inertia of the system decreases and the angular speed increases.
Center of Mass (CM)
the one point that moves the same path that a particle would move if subjected to the same net force for 2 particles, the CM lies closer to the one with the most mass
Suppose a solid uniform sphere of mass M and radius R rolls without slipping down an inclined plane starting from rest. The angular velocity of the sphere at the bottom of the incline depends on
the radius of the sphere
Elastic head on collisions
the relative sped fo the two objects after the collision has the same magnitude (but opposite direction) as before the collision, no matter the mass
You are lying in bed and want to shut your bedroom door. You have a bouncy "superball" and a blob of clay, both with the same mass. Which one would be more effective to throw at your door to close it?
the superball
Law of Conservation of Angular Momentum
the total angular momentum of a rotating object remains constant if the net torque on it is zero
Three cars, car X, car Y, and car Z, begin accelerating from rest at the same time. Car X is more massive than car Y, which is more massive than car Z. The net accelerating force exerted on each car is identical. After 10 seconds, which car has the most amount of momentum?
they all have the same amount of momentum
When a rigid object rotates about a fixed axis, what is true about all the points in the object?
they all have the same angular speed
During World War I, Germany used a "Big Bertha" cannon to hurl shells into Paris 30 miles away. This gun also had a very long barrel. What was the reason for using a long barrel in these guns?
to allow the force of the expanding gases from the gunpowder to act for a longer time
When you ride a bicycle, in what direction is the angular velocity of the wheels?
to your left
Impulse
we can get the same change in momentum with a large force acting for a short time, or a small force acting for a long time longer Δt = smaller F
Elastic Collision
when comparing the total kinetic energy just before collision with the total kinetic energy after collision and they are found to be the same, then the KE is conserved V121 = v12
A car speedometer that is supposed to read the linear speed of the car uses a device that actually measures the angular speed of the tires. If larger-diameter tires are mounted on the car instead, how will that affect the speedometer reading? The speedometer
will read low
An object at rest begins to rotate with a constant angular acceleration. If this object rotates through an angle θ in time t, through what angle did it rotate in the time ½t?
¼θ