Physics Quiz 2
A firecracker sitting on the ground explodes into two pieces. Immediately after the explosion, one of the pieces has momentum of 0.5 kg·m/s in the east direction. What is the momentum of the other piece?
0.5 kg·m/s west The momentum of the two pieces before the explosion was zero, so after the explosion, the total momentum must still be zero.
An object of mass m is traveling at constant speed v in a circular path of radius r. How much work is done by the centripetal force (force directed to center of circle) during one half of a revolution?
0 WORK DONE BY A CENTRIPETAL IS ALWAYS 0 because F is always perpendicular to v and displacement
If you hold a heavy weight over your head, the work you do __________.
Is zero.
Two friends are sitting in a stationary canoe. At t=t= 3s3s the person at the front tosses a sack to the person in the rear, who catches the sack 0.2 ss later. (Figure 1) 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
How does a car's kinetic energy change when it speeds up from 10 to 20 m/s?
It quadruples. KE= 1/2mv^2 KE is directly proportional to v^1/2
As an object moves around, on which quantities does the change in its gravitational potential energy depend? Choose all that apply.
Its change in height Its mass GPE- mgh so it depends on mass and height
The unit of kinetic energy is the _______.
Joule
The unit of work is the _______.
Joule
A block of mass 3 kg slides down a frictionless inclined plane of length 6 m and height 4 m. If the block is released from rest at the top of the incline, what is its speed at the bottom in m/s ?
KE the block gains the same as potential energy it loses (mgh) mgh=1/2mv^2 ........ v= sqrt(2gh) => sqrt(2*10*4)= 9m/s ANS: 9m/s
. A block of mass 3 kg slides down an inclined plane of length 6 m and height 4 m. If the force of friction on the block is a constant 16 N as it slides from rest at the top of the incline, what is its speed at the bottom in m/s ?
CONSERVATION OF ME Ki+Ui+W= Kf+Uf 0+mgh-FfL= 1/2mv^2+0 so V=Sqrt(2/m(mgh-Ffl)) = sqrt(2/3(3*10*4-16*6)) = 4m/s ans= 4m/s
A rock of mass 4 kg drops from the edge of a 40 meter high cliff, experiencing air resistance of average strength during the descent is 20 N. At what speed will the rock hit the ground in m/s ?
CONSERVATION OF ME Ki+Ui+W= Kf+Uf 0+mgh-FfL= 1/2mv^2+0 so V=Sqrt(2/m(mgh-Ffl)) = sqrt(2/4(40*10*4-20)) = 20m/s ans= 20m/s
A 3 kgkg cart rolling to the right at 7 m/sm/s runs into a 7 kgkg cart rolling to the left. After the collision, both carts are stationary. What was the original speed of the 7 kgkg cart? Express your answer with the appropriate units.
v2=3m/s They must have the same momentum... so 3kg*7m/s=21kgm/s 21/7= 3m/s
Under the influence of a force, an object of mass 4 kg accelerates from 3 m/s to 6 m/s in 8 s. How much work was done on the object during this time?
v= U+a*t a= (6-3)/8 = .375 m/s^2 F=ma so 4*.375= 1.5N Displacement= ut+1/2at^2 (3*8)+1/2(.375)*8^2 =36m Work = F*displacement 1.5*36= 54J ANSWER: 54J
A disk starting from rest undergoes a constant angular acceleration of 0.4 radians per second2 for 5 seconds. The final angular velocity is (in standard units)
b. 2 seconds
A 3 kg mass moving at +12 m/s has an inelastic collision with a 15 kg mass at rest. The final velocities of the combined 3 and 15 kg mass (in m/s):
https://www.chegg.com/homework-help/questions-and-answers/3-kg-mass-moving-12-m-s-inelastic-collision-15-kg-mass-rest-final-velocities-combined-3-15-q58969631?trackid=gj6LGxZE
Part complete 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.
The units of linear momentum are _________.
kg·m/s Because momentum is mass times velocity, it has units of kg times m/s.
An object's angular momentum is proportional to its __________.
moment of inertia
In an inelastic collision,
momentum is conserved
A 4.0-mm-diameter playground merry-go-round, with a moment of inertia of 300 kg⋅m2kg⋅m2 is freely rotating with an angular velocity of 2.5 rad/srad/s . Ryan, whose mass is 75 kgkg , runs on the ground around the outer edge of the merry-go-round in the opposite direction to its rotation. Still moving, he jumps directly onto the rim of the merry-go-round, bringing it (and himself) to a halt. How fast was Ryan running when he jumped on?
mvr= IW r= 4/2= 2m 75*v*2= 300*2.5 v= (300*2.5)/(75*2)= 5 ANSWER: 5.0 m/s
If you raise an object to a greater height, you are definitely increasing its __________.
gravitational potential energy
A car traveling at 100 km/hr strikes a bug and splatters it. The impulse is
greater for the bug The impulse is change in momentum it is larger for the bug bc they are smaller
A box of mass m slides down a frictionless inclined plane of length L and vertical height h. What is the change in its gravitational potential energy?
-mgh
If we half the speed of an object, but double the mass, then its new kinetic energy would be
.5x KE=1/2mv^2 & KE is directly proportional to speed^2 KE= 1/2 (m*2)(v/2)^2 =.5
A disk starting from rest undergoes a constant angular acceleration of 0.4 radians per second2. Through how many radians does it rotate in the first 5 seconds?
5 rad
The dimension of Power?
ALL: [kg][m2]/[s3], [M][L2]/[T3], Watt
A 1 kg mass of putty moving at 1 m/s collides and sticks to a 5 kg bowling ball that is initially at rest. After the collision the putty plus bowling ball move with a momentum of ______ kg m/s
ANS: 1 Init Momentum = 1kg*1m/s + 5kg*0m/s = 1kgm/s
A man steps off the back of a slowly moving skateboard in such a way that he has no velocity when he touches the ground (like a gymnast that lands with no forward or backward velocity). The skateboard will have then: a. slowed down b.
As he steps down, the moment of inertia will decrease so b, the platform will speed up ANS: the platform will speed up
On an energy diagram, where is a stable equilibrium point?
At a local minimum point
A stationary firecracker explodes into three pieces.One piece travels off to the east; a second travels to the north. (Figure 1) Which of the vectors of the figure could be the velocity of the third piece?
D
State clearly the principle of conservation of momentum. When is momentum NOT conserved?
For a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision. Momentum is not conserved if there is friction, gravity, or net force (net force just means the total amount of force). What it means is that if you act on an object, its momentum will change
Because of friction, rotational kinetic energy is not conserved while the disks' surfaces slip over each other. What is the final rotational kinetic energy, KfKfK_f, of the two spinning disks? Express the final kinetic energy in terms of ItItI_t, IrIrI_r, and the initial kinetic energy KiKiK_i of the two-disk system. No angular velocities should appear in your answer
KfKfK_f =Ki(ItIt+Ir)Ki(ItIt+Ir) Note that the final rotational kinetic energy is less than the initial rotational kinetic energy. Some of the initial kinetic energy gets converted into heat and sound as the frictional force between the disks (which causes a torque) stops their relative motion
In about 5 billion years, the sun will run out of fuel. It will gravitationally collapse in upon itself becoming a compact "white dwarf" star. Assuming that the mass is unchanged, but the sun shrinks to 1/100 its current size, by what factor will the moment of inertia change?
MRW^2=M(R/100)(w^2) W= 10w Anugular velocity = 10x
If the total energy of an object is zero, then a. kinetic energy must be zero b. the potential energy must be c. the speed must be zero d. the velocity must be zero, but the speed can be nonzero e. none of these
NONE OF THESE IF THE TOTAL ENERGY IS ZERO, BOTH KINETIC ENERGY AND POTENTIAL ENERGY = 0
An astronaut drops a rock from the top of a crater on the moon. When the rock is halfway down to the bottom of the crater, its speed is what fraction of its final impact speed?
Since the rock lost 1/2 the PE, its KE at halfway point is half the KE at impact KE is proportional to v^2, so KE at 1/2 way point = 1/2KE @impact ANS= 1/sqrt(2)
A force F of strength 20 N acts on an object of mass 3 kg as it moves a distance of 4 m. If F is perpendicular to the 4 m displacement, the work it does is equal to
Since there is no work done, work=0J (because perpendicular)
Which will reach the bottom of an inclined plane first?
Solid Sphere: has a smaller rotational inertia
In a collision that is not perfectly elastic, what happens to the mechanical energy of the system?
Some of the mechanical energy is converted into other forms. Energy gets stored as elastic PE so some energy is lost during a collision. Some ME is converted in various forms... it is not conserved
What is the impulse-momentum theorem?
The impulse-momentum theorem states that the impulse is equal to this change in momentum. The impulse-momentum theorem states that the change in momentum of an object equals the impulse applied to it. J = ∆p
Moment of Inertia SI unit
The unit of moment of inertia is a composite unit of measure. In the International System (SI), m is expressed in kilograms and r in metres, with I (moment of inertia) having the dimension kilogram-metre square. kg m^2
A 3 kg mass moving at +12 m/s has an elastic collision with a 15 kg mass at rest. The final velocities of the 3 and 16 kg masses respectively are (in m/s):
USE conservation of momentum 3*12= -3*v1+15*v2 u=12-5v 3(12)^2= 3(12-5v)^2+15v^2 v=4 u=12-20=8 ans= -8,4
Is Newton's formula: F=ma always true? If not, what is a more general statement that is always true?
When number of forces are acting on an object then momentum changes with respect to the time This is the most general statement F= dp/dt F=ma shouldnt happen because you are multiplying a scalar by a vector
Fred does his job. Harry does an identical job but 3× faster. Both jobs required the same amount of work, but had different amounts of
efficiency
A car having a total momentum of 4500 kg∙m/s moving at 2 m/s smashes into a tree, stopping in 2.5 seconds. The average force acting on the car during the collision is (units of N)
f= delta p/ delta t = Pf-Pi/delta t = 0-4500/ 2.5 = 1800N
A force of 200 N is required to keep an object sliding at a constant speed of 2 m/s across a rough floor. How much power is being expended to maintain this motion (in watts)?
p=Fv P= 200*2= 400W ANS= 400W
Impulse is ________.
the area under the force curve in a force-versus-time graph ?change in momentum?
Power is __________________.
the rate that the energy of a system is transformed Power is the rate at which work is done, which is also equal to the force times the speed
A disk rotates freely on a vertical axis with an angular velocity of 80 rpmrpm . An identical disk rotates above it in the same direction about the same axis, but without touching the lower disk, at 20 rpmrpm . The upper disk then drops onto the lower disk. After a short time, because of friction, they rotate together. Part complete The final angular velocity of the disks is
w1= 80rpm, w2=20rpm Total angular momentim L1= I1*W1 + I2*W2 = 80I+20I= 100I Total Final angular momentum L2=2IWf From law of conservation of angilar momentum L1=L2 100I=2IWf Wf= 100I/20I Wf (ANSWER)= 50rpm
Which of the following is an energy transfer?
work
While a person lifts a book of mass 2 kg from the floor to a tabletop 1.5 m above the floor, how much work does the gravitational force do on the book?
work done by grav force= mgh so 2*9.8*1.5= 29.4J => rounded to 30J
Consider a turntable to be a circular disk of moment of inertia ItItI_t rotating at a constant angular velocity ωiωiomega_i (note that angular velocities use the Greek letter omega and not double-u) around an axis through the center and perpendicular to the plane of the disk (the disk's "primary axis of symmetry") as shown in (Figure 1). The axis of the disk is vertical and the disk is supported by frictionless bearings. The motor of the turntable is off, so there is no external torque being applied to the axis. Another disk (a record) is dropped onto the first such that it lands coaxially (the axes coincide). The moment of inertia of the record is IrIrI_r. The initial angular velocity of the second disk is zero. There is friction between the two disks. After this "rotational collision," the disks will eventually rotate with the same angular velocity. What is the final angular velocity, ωfωfomega_f, of the two disks?
ωfωfomega_f = ItIt+IrωiItIt+Irωi
