exam 3
In the video, the two stuffed animals that rode on the turntable had the same __________ but had different __________.
Angular velocity, velocity
Moment of Inertia: The figure shows scale drawings of four objects, each of the same mass and uniform thickness, with the mass distributed uniformly. Which one has the greatest moment of inertia when rotated about an axis perpendicular to the plane of the drawing at point P?
B (q9 SM?)
A machine part is made up of two pieces, with centers of gravity shown in the figure.(Figure 1) Which point could be the center of gravity of the entire part?
D place between box and rectangle
You're carrying a 3.4-m-long, 24 kg pole to a construction site when you decide to stop for a rest. You place one end of the pole on a fence post and hold the other end of the pole 35 cm from its tip. How much force must you exert to keep the pole motionless in a horizontal position?
F = (24kg * 9.80m/s2 *3.4m)/(2(3.4m-0.35m) = 131 N
Equilibrium: A store's sign has a mass of 20 kg and is 3.0 m long. It is uniform, so its center of gravity is at the center of the sign. It is supported horizontally by a small loose bolt attached to the wall at one end and by a wire at the other end, as shown in the figure. What is the magnitude of the net force that the bolt exerts on the sign?
F=232.1 (q8 SM)
We often visualize the impulse by drawing a graph showing the force versus time. For a constant net force such as that used in the previous part, the graph showing the magnitude of the force versus time will look like the one shown in (Figure 1). Part B The magnitude of the net force versus time graph has a rectangular shape. Often in physics geometric properties of graphs have physical meaning.
For this graph, the area of the rectangle corresponds to the impulse.
The 680 g bar is rotating as shown in (Figure 1). What is the angular momentum of the bar about the axle? Recall the moment of inertia of a bar rotating with the axle at center is (1/12 x mass x length-squared) and a bar rotating with the axle on one side is (1/3 x mass x length-squared).
I=1/2(680*10^-3kg)(2m)^2 = 0.2266kgm L=(0.2266)(120rpm)(2pi rad/1rev)(1m/60 sec) = 2.847kgm^2/s
A 60 g tennis ball with an initial speed of 34 m/s hits a wall and rebounds with the same speed. (Figure 1) shows the force of the wall on the ball during the collision. What is the value of Fmax, the maximum value of the contact force during the collision?
Imp=0.06kg*2*34m/s=4.08kgm/s A=2*1/2*F*0.002s =(F*0.004s)/4.08kgm/s =1020N
A 4.0 kg block of wood sits on a frictionless table. A 3.0 g bullet, fired horizontally at a speed of 430 m/s , goes completely through the block, emerging at a speed of 220 m/s .What is the speed of the block immediately after the bullet exits?
Mi= 4*0+(3/1000)*430 Mi=1.29 Mf=4v+(3/1000)*220 Mf=4x+(33/50) 1.29=4x+(33/50) x=0.16m/s
The component of the momentum of piece B, pBx,f, is measured to be +500 kg⋅m/s after the explosion. Find the component of the momentum pAx,f of piece A after the explosion.
Paf=-Pbf so -500kg*m/s
Springs can stretch; so can different materials, including
Rubber, Glass, Steel
A vendor hangs an 8.2 kg sign in front of his shop with a cable held away from the building by a lightweight pole. The pole is free to pivot about the end where it touches the wall, as shown in (Figure 1). What is the tension in the cable?
T=2*8.2*9.8 = 160.72N (has a triangle with 60º so Tcos60=mg?)
Which of the following statements correctly describes the system shown in the figure?
The angular acceleration of the pulley is nonzero.
Rank the automobiles based on the magnitude of the force needed to stop them, from largest to smallest.
The correct ranking cannot be determined.
When we say that momentum is "conserved," we mean
The momentum of an isolated system is constant.
For an object to be in static equilibrium, the net force must be equal to zero and
The net torque must be equal to zero.
When we draw a diagram of the forces acting on an extended object, the tail of the force vector for the weight should be at
The object's center of gravity.
What happens when block B moves downward?
The right cord pulls on the pulley with greater force than the left cord.
Is the spring constant of these smaller springs larger, smaller, or the same as the spring constant of the original spring? Choose the correct explanation.
The spring constant of each half will be twice the spring constant of the original long spring since it will stretch only half as much under the same tension.
If you kick a ball, you apply an impulse. The impulse is equal to
change in momentum of ball
Where is the center of gravity of the man doing the classic yoga poses shown in (Figure 1)?
circle on mans upper thigh that is on the ground
During the explosion, is the magnitude of the force of piece A on piece B greater than, less than, or equal to the magnitude of the force of piece B on piece A?
equal to
The cheater pipe ____the wrench in the radial direction, providing ____a moment arm for the force you exert. For a given force the torque exerted with the cheater pipe is _____.
extends, larger larger
Curling is a sport played with 20 kg stones that slide across an ice surface. Suppose a curling stone sliding at 2.5 m/s strikes another stone and comes to rest in 2 ms .
f(2*10^-3)=-20*2.5 f=-25000N f=25,000N
A child is sliding on a sled at 1.1 m/s to the right. You stop the sled by pushing on it for 0.40 s in a direction opposite to its motion. If the mass of the child and sled is 37 kg , what is the magnitude of the average force you need to apply to stop the sled? Use the concepts of impulse and momentum.
f= (37*1.1)/0.4 = 101.75N
If the raindrop comes to rest in 0.37 ms, what is the magnitude of the average force of the impact?
f=(11.34*10^-6kg/ms)/(0.37*10^-3s) f=0.306N
If the sum of both the external torques and the external forces on an object is zero, then the object must be at rest.
false
If the sum of the external forces on an object is zero, then the sum of the external torques on it must also be zero.
false
If the sum of the external torques on an object is zero, then the sum of the external forces on it must also be zero.
false
A man is holding the yoga position shown in (Figure 1). The center of gravity of the combination of his head, arms, and torso is shown as a red symbol on his torso; the center of mass of his legs and feet is a red symbol on his legs. Which of positions A through D corresponds to the center of mass of his entire body?
figure A
A stationary firecracker explodes into three pieces.One piece travels off to the east; a second travels to the north. Which of the vectors of the figure could be the velocity of the third piece?
first piece is east and second piece is north so vector is southwest (D)
Which of the graphs corresponds to angular position versus time?
graph A (linear pos)
Which of the following graphs corresponds to angular velocity versus time?
graph C (straight line pos)
Which of the graphs corresponds to x position versus time?
graph f (squiggle pos to neg)
Which of the graphs corresponds to y velocity versus time?
graph f (squiggle pos to neg)
If you raise an object to a greater height, you are increasing its __________.
gravitational potential energy
The toy on a spring illustrated energy conversion among what different forms?
gravitational potential energy, kinetic energy, and elastic potential energy
If a system is isolated, the total energy of the system ________.
is constant
What is the magnitude of the impulse delivered to your roof?
j=14*10^-6(8.1) j=113.4*10^-6N-s
A 3 kg cart rolling to the right at 5 m/s runs into a 5 kg cart rolling to the left. After the collision, both carts are stationary. What was the original speed of the 5 kg cart?
(3*5)+(5v)=(3+5)(0) 15+5v=0 v=3 m/s
What is the movement direction of the resulting 61 g blob of clay?
(35*2.6)/(26*3.5)=tanx x=45º
A 59 kg diver stands at the end of a 32 kg springboard, as shown in the figure. The board is attached to a hinge at the left end but simply rests on the right support. What is the magnitude of the vertical force exerted by the hinge on the board?
(59*9.8 = 578.2N) pic has 3m in center so half of board is 1.5m
A 79 kg baseball player jumps straight up to catch a hard-hit ball. If the 140 g ball is moving horizontally at 29 m/s , and the catch is made when the ballplayer is at the highest point of his leap, what is his speed immediately after stopping the ball?
0.14*29=(79+0.14)V v=0.051 m/s
A student gives a steady push to a ball at the end of a massless, rigid rod for 1 ss, causing the ball to rotate clockwise in a horizontal circle as shown in (Figure 1). The rod's pivot is frictionless. Choose a correct graph of the ball's angular velocity as a function of time for the first 3ss of the ball's motion. By convention, clockwise rotations are negative and counterclockwise rotations are positive.
line stops at 1 then goes straight
Springs: An ornament of mass 40.0 g is attached to a vertical ideal spring with a force constant (spring constant) of 20.0 N/m. The ornament is then lowered very slowly until the spring stops stretching. How much does the spring stretch?
mg=(60*10^-3*9.8)/20 = 0.0196m
Where is the center of gravity of the woman doing the classic yoga poses shown in (Figure 2)?
near appendix area
If an object is rotating clockwise, this corresponds to a _____ angular velocity.
negative
Assume that a pitcher throws a baseball so that it travels in a straight line parallel to the ground. The batter then hits the ball so it goes directly back to the pitcher along the same straight line. Define the direction the pitcher originally throws the ball as the +x direction. The impulse on the ball caused by the bat will be in the
negative x direction
Viewed from somewhere in space above the north pole, would a point on the earth's equator have a positive or negative angular velocity due to the earth's rotation?
positive
A 26 g ball of clay traveling east at 3.5 m/s collides with a 35 g ball of clay traveling north at 2.6 m/s .
q 93-94
A giant "egg" explodes as part of a fireworks display. The egg is at rest before the explosion, and after the explosion, it breaks into two pieces, with piece B moving in the positive x direction. The masses of both pieces are indicated in (Figure 1), shown traveling in opposite directions.
q102-104
A large raindrop--the type that lands with a definite splat--has a mass of 0.014 g and hits your roof at a speed of 8.1 m/s.
q97-98
Learning Goal: To understand the relationship between force, impulse, and momentum. (→ vector) The effect of a net force ΣF→ acting on an object is related both to the force and to the total time the force acts on the object. The physical quantity impulse J→ is a measure of both these effects. For a constant net force, the impulse is given by J→=F→Δt. The impulse is a vector pointing in the same direction as the force vector. The units of J→ are N⋅s or kg⋅m/s Recall that when a net force acts on an object, the object will accelerate, causing a change in its velocity. Hence the object's momentum (p→=mv→) will also change. The impulse-momentum theorem describes the effect that an impulse has on an object's motion: Δp→=J→=F→Δt. So the change in momentum of an object equals the net impulse, that is, the net force multiplied by the time over which the force acts. A given change in momentum can result from a large force over a short time or a smaller force over a longer time.
questions 52-56
Six automobiles are initially traveling at the indicated velocities. The automobiles have different masses and velocities. The drivers step on the brakes and all automobiles are brought to rest.
questions 58-60
To win a prize at the county fair, you're trying to knock down a bowling pin by hitting it with a thrown object.
questions 66-67
If you free the cork in a highly pressurized champagne bottle, the resulting launch of the cork will, in principle, cause the bottle to recoil. A filled champagne bottle has a mass of 1.8 kg. The cork has a mass of 7.5 g and is launched at 18 m/s.
questions 74-75
To throw the discus, the thrower holds it with a fully outstretched arm. Starting from rest, he begins to turn with a constant angular acceleration, releasing the discus after making one complete revolution. The diameter of the circle in which the discus moves is about 1.7 m. If the thrower takes 1.1 s to complete one revolution, starting from rest, what will be the speed of the discus at release?
r=0.85 w=4pi/(1.1)^2 v= (0.85/1.1)*4pi = 9.71m/s
The angular displacement of a rotating object is measured in _____.
radians
Should you choose to throw a rubber ball, which will bounce off the pin, or a beanbag, which will strike the pin and not bounce? Assume the ball and beanbag have equal size and weight.
rubber ball
What is the magnitude of the momentum | p→A,| of piece A before the explosion?
since the egg is at rest the momentum is zero
What is the period of the motion?
t=60/33rps so =1.812s
A standard four-drawer filing cabinet is 52 inches high and 15 inches wide. If it is evenly loaded, the center of gravity is at the center of the cabinet. A worker is tilting a filing cabinet to the side to clean under it. To what angle can he tilt the cabinet before it tips over?
tan(52/15)=73.9º 90-73.9= 16.1º
A net torque applied to an object causes __________.
the angular velocity of the object to change
In this video, we use the law of conservation of energy. For the systems we consider,
the initial total energy of the system equals the final total energy of the system.
Which factor does the torque on an object NOT depend on?
the object's angular velocity
Rasheed and Sofia are riding a merry-go-round that is spinning steadily. Sofia is twice as far from the axis as is Rasheed. Sofia's angular velocity is ______ that of Rasheed.
the same as
If a ball rolls around a circular track with a of diameter 0.5 m with an angular velocity of 6π rad/s. What is the period of the motion?
theta=2pi t=(2pi/6pi) = 1/3s
Rotational Dynamics: A force of 16.88 N is applied tangentially to a wheel of radius 0.340 m and causes an angular acceleration of 1.20 rad/s2. What is the moment of inertia of the wheel?
torque= 16.88(0.340)=5.73 N-m I=5.73/1.20= 4.78kg*m^2
If an object remains at rest, then the sum of both the external torques and the external forces on the object must be zero.
true
A man standing on very slick ice fires a rifle horizontally. The mass of the man together with the rifle is 70 kg , and the mass of the bullet is 10 g . If the bullet leaves the muzzle at a speed of 500 m/s , what is the final speed of the man?
v2=10*500/70*1000 =0.0714m/s
If the bottle could move freely, with what speed would it recoil?
v= (0.0075kg*18m/s)/ 1.8kg = 0.075m/s
Now assume that the pitcher in Part D throws a 0.145-kg baseball parallel to the ground with a speed of 32 m/s in the +x direction. The batter then hits the ball so it goes directly back to the pitcher along the same straight line. What is the ball's x-component of velocity just after leaving the bat if the bat applies an impulse of −8.4N⋅s to the baseball?
v=(-8.4/0.145)+32 = -25.93 m/s
What is the speed of the resulting 61 g blob of clay
v=(26*3.5)/(61*cos45) v=2.11m/s
What is the angular velocity of the wheel at 15 s?
w=(62.5-75)/(15-10)= -2.5 rad/s
What is the maximum speed of a point on the outside of the wheel 15 cm from the axle?
w=(72-25)/(10-0) = 5rad/s v=5*(15/100) = 0.75m/s
The lightweight wheel on a road bike has a moment of inertia of 0.097 kg⋅m2. A mechanic, checking the alignment of the wheel, gives it a quick spin; it completes 5 rotations in 2.4 s. To bring the wheel to rest, the mechanic gently applies the disk brakes, which squeeze pads against a metal disk connected to the wheel. The pads touch the disk 7.1 cm from the axle, and the wheel slows down and stops in 1.4 s. What is the magnitude of the friction force on the disk?
w=5*2pi/2.4=13.089 rad/s f*0.071*1.4=0.097*(13.089) f=12.78N
Ice skaters often end their performances with spin turns, where they spin very fast about their center of mass with their arms folded in and legs together. Upon ending, their arms extend outward, proclaiming their finish. Not quite as noticeably, one leg goes out as well. Suppose that the moment of inertia of a skater with arms out and one leg extended is 3.0 kg⋅m2 and for arms and legs in is 0.80 kg⋅m2 . If she starts out spinning at 4.3 rev/s , what is her angular speed (in rev/s) when her arms and one leg open outward?
0.80*4.3=3*x x=1.146 rev/sec
Torque: As shown in the figure, a given force is applied to a rod in several different ways. In which case is the torque about the pivot P due to this force the greatest?
1 (study q7 more)
A child on a merry-go-round takes 2.6 s to go around once. What is his angular displacement during a 1.0 s time interval?
1 round = 2 pi rad = 52.6 sec 1 sec= 2pi/2.6 = 2.42 rad
Rank these automobiles based on the magnitude of the impulse needed to stop them, from largest to smallest.
1. (1000kg,20m/s) 1. (4000kg,5m/s) 2.(1000kg,10m/s). 2.(2000kg,5m/s) 2.(500kg,20m/s). 3.(500kg,10m/s)
Rank these automobiles based on the magnitude of their momentum before the brakes are applied, from largest to smallest.
1. (1000kg,20m/s) 1. (4000kg,5m/s) 2.(1000kg,10m/s). 2.(2000kg,5m/s) 2.(500kg,20m/s). 3.(500kg,10m/s)
Two balls are hung from cords. The first ball, of mass 1.4 kg , is pulled to the side and released, reaching a speed of 2.1 m/s at the bottom of its arc. Then, as shown in the figure, it hits and sticks to another ball. The speed of the pair just after the collision is 1.4 m/s. What is the mass of the second ball?
1.4=1.4*2.1/(1.4+m2) m2= 0.70 kg
What is the magnitude of the torque about his shoulder if he holds his arm straight out to his side, parallel to the floor?
1.5 * 0.70*9.8+4*0.35*9.8= 24.01 N-m
In Parts A, B, C consider the following situation. In a baseball game the batter swings and gets a good solid hit. His swing applies a force of 12,000 N to the ball for a time of 0.70×10^−3s. Part A Assuming that this force is constant, what is the magnitude J of the impulse on the ball?
12,000*0.0007 = 8.4Ns
The figure below shows two blocks suspended by a single cord over a pulley. (Figure 1) The mass of block B is twice the mass of block A, while the mass of the pulley is equal to the mass of block A. The blocks are let free to move and the cord moves on the pulley without slipping or stretching. There is no friction in the pulley axle, and the cord's weight can be ignored.
30-31
An athlete at the gym holds a 1.5 kg steel ball in his hand. His arm is 70 cm long and has a mass of 4.0 kg .
33-34
Constant Angular Acceleration: A wheel accelerates from rest to 59 rad/s at a uniform rate of 58 rad/s2. Through what angle (in radians) did the wheel turn while accelerating?
59^2=0+2*58*theta theta=30rad
What is the angular displacement of the wheel between t = 5 s and t = 15 s?
5@50 and [email protected] 62.5-50=12.5
A record rotates on a turntable at 33 rpm
8-9
First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the question at right. You can watch the video again at any point. Suppose we replace the mass in the video with one that is four times heavier. How far from the free end must we place the pivot to keep the meter stick in balance?
90 cm (10 cm from the weight)
In (Figure 1), force F2 acts half as far from the pivot as F1. What magnitude of F2 causes the net torque on the rod to be zero?
=sqrt2 * 20 = 28.28N
Two friends are sitting in a stationary canoe. At t=3s the person at the front tosses a sack to the person in the rear, who catches the sack 0.2 s later. 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
(Figure 1) shows two blocks sliding on a frictionless surface. Eventually the smaller block overtakes the larger one, collides with it, and sticks. Suppose that M=6m. What is the speed of the two blocks after the collision?
(2m+6m)/(6m+m) =8vi/7
While working on her bike, Amanita turns it upside down and gives the front wheel a counterclockwise spin. It spins at approximately constant speed for a few seconds. During this portion of the motion, she records the x and y positions and velocities, as well as the angular position and angular velocity, for the point on the rim designated by the yellow-orange dot in the figure. (Figure 1) Let the origin of the coordinate system be at the center of the wheel, the positive x direction to the right, the positive y position up, and the positive angular position counterclockwise. The graphs(Figure 2) begin when the point is at the indicated position. One graph may be the correct answer to more than one part.
13-16
Divers change their body position in midair while rotating about their center of mass. In one dive, the diver leaves the board with her body nearly straight, then tucks into a somersault position. If the moment of inertia of the diver in a straight position is 14 kg⋅m^2 and in a tucked position is 4.0 kg⋅m^2 , by what factor is her angular velocity when tucked greater than when straight?
14/4 = 3.5
What is the net torque on the bar shown in (Figure 1), about the axis indicated by the dot? Suppose that F = 16 N
16*0.75 = 12N-m
(Figure 1) shows the angular position of a potter's wheel.
19-21
What is the magnitude of the torque about his shoulder if he holds his arm straight, but 50 ∘∘ below horizontal?
24.01cos50=15.43N-m
Is this something you are likely to notice?
A person holding the bottle as the cork pops is likely to feel this recoil.
You must lean quite far forward as you rise from a chair (try it!). Choose the correct explanation.
Your center of gravity must remain over a region of support (your feet). As you rise your rear end is behind your feet so you must lean forward to compensate.
The impulse exerted on the bowling pin equals the negative of the___ of the projectile during collision. The rubber ball and beanbag would start with the same momentum, but the rubber ball would have a greater ____ because it would bounce off and so _____. The beanbag would continue to move in the same direction. Thus a rubber ball would exert a greater impulse on the bowling pin.
a. change in momentum b. change in momentum, its direction would change
In the video, we looked at the problem of balancing a pencil on your fingertip, which is easy for a long pencil, hard for a short pencil. If you consider a long and a short pencil tipped to the side, the __________ of the shorter pencil is larger.
angular acceleration
If both the graph representing the constant net force and the graph representing the variable net force represent the same impulse acting on the baseball, which geometric properties must the two graphs have in common?
area (When the net force varies over time, as in the case of the real net force acting on the baseball, you can simplify the problem by finding the average net force F→avg acting on the baseball during time Δt This average net force is treated as a constant force that acts on the ball for time Δt The impulse on the ball can then be found as J→=F→avgΔt.
What is the angular speed in rad/s?
as= (2*3.14*33)/60 so = 3.456rad/s
The graph in (Figure 1) shows the angular velocity of the crankshaft in a car. Choose the correct graph of the angular acceleration of the crankshaft versus time.
bottom line: @-100 goes up at 2 middle:@0 from 2-4 straight top: @50 from 4-7
