•In two dimensions, an object's displacement is a vector:
•The velocity vector is simply the displacement vector multiplied by the scalar (1/change in t)
•Consequently the velocity vector points in the direction of the displacement.
velocity vector= d vector (both x and y components)/ change in time
question
the velocity vector points in the direction of the
answer
displacement
question
Acceleration in Two Dimensions
answer
•The vector definition of acceleration is a straightforward extension of the one-dimensional version: change in acceleration vector=change in velocity vector (vf-vi)/ change in time
•There is an acceleration whenever there is a change in velocity. Velocity can change in either or both of two possible ways:
1. The magnitude can change, indicating a change in speed.
2. The direction of motion can change, indicating a change in direction.
question
•There is an acceleration whenever there is a change in velocity. Velocity can change in either or both of two possible ways:
answer
•There is an acceleration whenever there is a change in velocity. Velocity can change in either or both of two possible ways:
1. The magnitude can change, indicating a change in speed.
2. The direction of motion can change, indicating a change in direction.
question
A particle undergoes acceleration a ? while moving from point 1 to point 2. Which of the choices shows the velocity vector (v_2 ) ? as the object moves away from point 2
answer
find Vf component (y component) of acceleration vector
question
The diagram shows three points of a motion diagram. The particle changes direction with no change of speed. What is the acceleration at point 2?
answer
need the acceleration vector which makes the two velocity vectors equal (both the V1 from 1-2 and the Vf that is drawn in)
question
Reminder of Motion Diagram for Circular Motion
answer
acceleration is perpendicular to velocity
-velocity is tangent to the circle and a is perpendicular to v, pointing toward the center
to find the change in velocity vector, subtract the velocity at point 1 from the velocity at point2
-the acceleration vector points in the same direction as the change in velocity vector, so toward the center of the circel
question
period-T
answer
time it takes object to complete a full circle [T]=S
question
frequency-f
answer
the number of revolutions per time period 1/s= hertz Hz
question
centripetal acceleration
answer
acceleration toward the center of a curved or circular path
m/s^2
b/c is V^2/r which is (m^2/s^2)/m
question
circumference
answer
2?r or 2d
question
A car is turning a tight corner at a constant speed. A top view of the motion is shown in the figure. The velocity vector for the car points to the east at the instant shown. The direction of the acceleration is
a.N
b.E
c.S
d.W
answer
south
question
A runner is running at a uniform pace on a circular track of radius 50 m. It takes her 314 seconds to complete one lap. Determine her speed.
Forces are pushes or pulls. Every force acts on an object. Every force has an agent—something that does the pushing or pulling.
question
(just one for us) Long-range or non-contact forces
answer
gravitational (weight of object)
question
contact forces
answer
These exist only as the objects are touching each other.
v actual touching—from a shove or a kick
v friction
v tension in a rope or chain
v forces from floors, tables, or walls
v drag forces such as air resistance
thrust from rocket engines
NO Force is objects are NOT touching--it's the interaction that is the force
question
Newton's First Law of Motion
Law of Inertia
answer
If the net force acting on an object is zero.
• and if this object is at rest, it will remain at rest.
• and if this object is in motion, it will continue to move in a straight line at a constant speed.
question
thought experiment: somebody has a hockey stick and a hockey puck-can give same amount of velocity to object when they hit it
-in the grass, hit hockey puck
-on rough ice
-smooth ice
-frictionless ice
answer
stops b/c of friction
-goes farther, but still slows to a stop
-on smooth goes farther
-on frictionless, speed never changes and once hickey stick isn't touching it, the net force is zero and the speed is maintained-would go forever
question
HP nightbus movie example
answer
Harry standing with net force of zero, bus moves forward and he slams into back b/c not enough friction
-Harry then moves at same constant speed as bus
-bus slams on brakes, HP moves forward and slams into front
question
Net force (a vector)
answer
vFind the vector sum of all forces exerted on an object.
? not interested in forces exerted by the object.
vThe vector sum may be expressed in component form or as a magnitude and direction.
question
The figure shows the top view of a box, in which only the forces shown are acting on the box. Determine the net force in component form.
5N to left and 10N to R
answer
5N to right
question
The figure shows the top view of a box, in which only the forces shown are acting on the box. Determine the net force in component form.
4N up, 6N left, 8N down
answer
6N left and 4N down in component form
question
Newton's Second Law, preliminary
answer
If the net force on an object is not zero, the velocity of the object changes.
-change in velocity per unit of time is acceleration
-acceleration has the same direction as the net force
question
acceleration has the same direction as the
answer
net force
question
The figure shows the top view of a box, in which only the forces shown are acting on the box. Determine the net force in component form. This box is moving to the right. Which of the motion diagrams agrees with the motion of the block.
5N to left and 10N to right
answer
net force in component form
direction of net force gives direction of acceleration
net force is 5N to the right, motion diagram shows speeding up
question
The figure shows the top view of a box, in which only the forces shown are acting on the box. Determine the net force in component form. This box is moving to the left. Which of the motion diagrams agrees with the motion of the block.
5N to left and 10N to right
answer
but box is moving to L
-negative velocity (because moving to L)
-acceleration is 5n to the R, so opposite signs, so slowing down
question
does the motion of the object have to be in the direction of the net force?
answer
no, could be, but not always
question
Weight
answer
•The gravitational pull of the earth on an object on or near the surface of the earth is called weight.
•The agent for the weight forces is the entire earth pulling on an object.
•An object's weight vector always points vertically downward, no matter how the object is moving.
question
Spring Force
answer
•Springs come in in many forms. When deflected, they push or pull with a spring force.
object=box
agent=spring
question
Tension Force
answer
•When a string or rope or wire pulls on an object, it exerts a contact force that we call the tension force.
The direction of the tension force is always in the direction of the string or rope
agent=rope acting on the sled
-rope exerts a tension force on the sled
question
Normal Force
answer
•The force exerted on an object that is pressing against a surface is in a direction perpendicular to the surface.
•The normal force is the force exerted by a surface (the agent) against an object that is pressing against the surface.
agent: desk
object: book
question
Friction can occur when object is ____ or _____
answer
moving or sedentary
question
if sled is moving to the right but slowing down, V vector is directed toward the right, but fk vector is to the ___ b/c a kinetic friction force
answer
left b/c kinetic friction force is slowing the sled down
question
woman pulling to the left, but the crate does not move b/c
answer
a static friction force directed to the right opposes that motion
question
Drag
answer
•The resistive force of a fluid (like air or water) on a moving object is called drag.
•Like kinetic friction, drag points opposite the direction of motion.
You can neglect air resistance in all problems unless a problem explicitly asks you to include it
question
Thrust
answer
•Thrust is a force that occurs when a jet or rocket engine expels gas molecules at high speed. (octopus or squid also)
•Thrust is a force opposite the direction in which the exhaust gas is expelled.
object=rocket
agent=molecules in rocket fuel as they come out
question
A red-tailed hawk that weighs 8 N is gliding at constant speed. What is the net force acting on the hawk?
a.8 N in the downward direction
b.8 N in the direction the hawk is flying
c.8 N in the upward direction
d.0 N
Draw the motion diagram for the hawk as it is flying with constant speed.
answer
net force is zero on the hawk, because speed is constant
dots are equally spaced
question
Emily pushes on a box with a horizontal force of 10 N. The box does not move. What is the net force on the box?
a.10 N in the direction of the push
b.0 N
c.10 N opposite the direction of the push
d.10 N down
answer
net force is 0 N because static friction in 10N in opposite direction of push
question
constructing a free body diagram
A bungee jumper has jumped off of a bridge and is nearing the bottom of her fall. What forces are exerted on the bungee jumper?
answer
-taking/freeing from the context of the problem and representing environment with forces
object is bungee jumper
tension from rope cuts through circlr
question
steps of free body diagram
answer
1. draw boundary around man (what we're studying) pin point the object and its environment
2. ID what forces: name and label--tension from rope, earth on man
3. name and label long range force (not physical)--gravity
question
Ron pushes to the right on a box. The box does not move.
Draw a free body diagram of the box. Identify the object being acted on AND the agent of the force.
answer
agent is ron
object is box
question
1Workbook Chapter 4 #21 You are going to toss a rock straight up into the air by placing it on the palm of your hand (you're not gripping it), then pushing your hand up very rapidly. You may want to toss an object into the air to help you think about the situation. Draw a picture to help you identify the forces. Draw a free body diagram and label the forces for the following situations. Be sure to identify the agent of the force and the object being acted on.
a.As you hold the rock at rest on your palm, before moving your hand.
b.As your hand is moving up but before the rock leaves your hand.
c.One-tenth of a second after the rock leaves your hand.
d.After the rock has reached its highest point and is now falling straight down.
answer
a. agent: normal force of hand on object: rock
equal vector length of both Normal and Weight b/c net force is zero
b. weight force is the same, but N is longer
c. no N force, b/c no contact with the hand; just W
d. only thing acting on it is weight force
question
An elevator, lifted by a cable, is moving upward and slowing.
•What is the direction of the acceleration?
•What is the direction of the net force?
•Which is the correct free-body diagram?
Be prepared to identify the agent of any forces shown in your selected diagram.
answer
-negative
negative, down (direction of acceleration has to be the direction of the net force)
T rope up and W down which is longer
question
A ball, hanging from the ceiling by a string, is pulled back and released. We are interested in the time just after the ball is released.
•What is the direction of the acceleration?
•What is the direction of the net force?
•Which is the correct free-body diagram?
Be prepared to identify the agent of any forces shown in your selected diagram.
answer
positive
pos
question
A car is parked on a hill.
•What is the direction of the acceleration?
•What is the direction of the net force?
•Which is the correct free-body diagram?
Be prepared to identify the agent of any forces shown in your selected diagram.
answer
tilted axis
-force from car touching incline
-acceleration is zero b/c not moving
-net force is thus zero
-friction force points uphill b/c if started, would roll down, so friction force is opposite; normal force points up, W straight down
question
A car is towed to the right at constant speed.
•What is the direction of the acceleration?
•What is the direction of the net force?
•Which is the correct free-body diagram?
Be prepared to identify the agent of any forces shown in your selected diagram.
answer
zero
zero
D-all forces are equal, b/c net force is zero
question
newton's second law
answer
•A force causes an object to accelerate.
•The acceleration a is directly proportional to the force F and inversely proportional to the mass m:
acceleration=fnet/mass
•The direction of the acceleration is the same as the direction of the force:
question
If a golf ball and bowling ball have same hit/Fnet, the ____________________ ball has larger acceleration.
answer
golf ball has larger acceleration b/c smaller mass
question
what is a Newton?
answer
unit of force
[F-fnet]=kg x m/s^2 = N
question
At the instant that these two forces are applied, the 10 kg box has a velocity of zero. What is its velocity 5 seconds later?
5N to left and 10 N to right
answer
net force is 5N to the right
mass is 10kg
acceleration is 5N/10kg = 0.5 m/s^2
now back to constant acceleration to find velocities
change in V = (0.5 m/s^2)(5s) = + 2.5 m/s at 5 seconds
question
t the instant that these two forces are applied, the 10 kg box has a velocity of -4 m/s.
What is it's velocity 5 seconds later?
5N to left and 10N to right
answer
acceleration is 0.5 m/s^2
velocity calculated before as +2.5m/s
change in V = Vf-Vi
Vf- (-4)=2.5m/s
question
A 5-kg block is traveling such that v_x=+4 m/s and v_y=+4 m/s. Two forces are then applied as shown in the diagram.
•What are the x- and y- components of the acceleration?
What are the x- and y- components of the velocity in 5 seconds?
10N up and 20N to the right
answer
accel in y: 10N/5kg= 2 m/s^2
accel in x: 20/5= 4
velocity:
in y: 2 m/s^2 (5s)=change in velocity=10m/s
started at v=4
vf in y=14m/s
in x: change in velocity=(4m/s^2)(5s)= 20 m/s
vf= 20 + 4 = 24m/s
question
A 10-kg box is traveling to the right with a speed of 30 m/s.
•What are the x- and y- components of the acceleration?
•
•What are the x- and y- components of the velocity after 2 seconds?
force 100 N down
answer
acceleration in y: -100N/10kg = -10m/s
acceleration in x=0 (constant speed)
velocity after 2 seconds
in y: change in velocity= acceleration x change in time
=(-10m/s^2)(2s)= -20m/s
Vf-0=20m/s
in x: chnage in V= 0x2=0
Vf-30=0 vf=30m/s
question
Scallops eject water from their shells to provide a thrust force. The graphs shows a smoothed graph of actual data for the initial motion of a 25 g scallop speeding up to escape a predator. What is the magnitude of the net force needed to achieve this motion? How does this compare to the 0.25 N weight of the scallop?
answer
given velocity
-find a to find net force
scallop weighs 25 g--must be in KG--0.025kg
acceleration= (0.2-0)/(0.2-0) = 1m/s^2
a= fnet/m
1=fnet/0.025kg = 0.025N
how does this compare to the 0.25 N weight of scallop? RATIO: divide 0.025N/0.25N = 0.1
how big is the force relative to the weight force
question
Newton's Third Law
answer
•Motion often involves two or more objects interacting with each other.
•As the hammer hits the nail, the nail pushes back on the hammer.
•A bat and a ball, your foot and a soccer ball, and the earth-moon system are other examples of interacting objects.
question
Interacting Objects: interaction and action/reaction pair
answer
•An interaction is the mutual influence of two objects on each other.
•The pair of forces shown in the figure is called an action/reaction pair.
question
•An action/reaction pair of forces exists as a ___, or ___ at all.
answer
pair or not at all
question
§The two members of an action/reaction pair act on ___ _____ objects.
§The two members of an action/reaction pair point in ____ directions and are ____ in magnitude
answer
Newton's third law Every force occurs as one member of an action/reaction pair of forces.
§The two members of an action/reaction pair act on two different objects.
§The two members of an action/reaction pair point in opposite directions and are equal in magnitude.
question
A bat hits a ball. Imagine you are viewing this from the end of the bat.
•Draw a free body diagram of the bat.
•
•Draw a free body diagram of the ball.
•
•Identify third law pairs.
•
What is the third law pair for the weight of the bat?For the ball?
answer
FB diagram of bat: Fball on bat to left nad W down
FB of ball: F bat on ball to right and W down
F bat on earth up from earth and F ball on earth up from earth
3rd law pairs: Fball on bat and Fbat on ball
-Fball on earth
Fbat on earth
person holding bat: F person on bat and third law pair is Fbat on person
question
A mosquito runs head-on into a truck. Splat! Which is true during the collision?
A. The mosquito exerts more force on the truck than the truck exerts on the mosquito.
B. The truck exerts more force on the mosquito than the mosquito exerts on the truck.
C. The mosquito exerts the same force on the truck as the truck exerts on the mosquito.
D. The truck exerts a force on the mosquito but the mosquito does not exert a force on the truck.
E. The mosquito exerts a force on the truck but the truck does not exert a force on the mosquito.
answer
C. The mosquito exerts the same force on the truck as the truck exerts on the mosquito.
question
mass vs weight
answer
Mass is an inherent property of an object. The object can be relocated and the mass will not change.
Weight is the force on the object due to the gravitational attraction of a large astronomical body. That body can be the Earth, the moon, Mars, etc. Weight is not an inherent property of the object.
Mass and weight are linked through w=mg. Here on earth, we sometimes interchange the words in our everyday conversation.
question
Mass and weight are linked through
answer
Mass and weight are linked through w=mg
question
1 lb in N
answer
4.45 N
question
110lb person in N
1lb object in N
answer
500N
5N
question
Newton's Universal Law of Gravitation
answer
Mass attracts mass.
F(1 on 2)= F(2 on 1)=G (m_1 m_2)/r^2
Where G is the universal gravitation constant
G=6.67 x 10^(-11) (N m^2)/?kg?^2 .
m1 and m2 are masses.
r is the distance between the masses.
question
what is Fearth on book?
answer
Fe on b= 6.67 x 10^-11 Nm^2/kg^2 ((5.98x10^24 x 1.0kg)/(6.37 x 10^6 m)^2) = 9.8N (acceleration due to gravity comes from this
question
When you are near an astronomical body:
F=m (G m_(ast body)/r^2 )
answer
And we call the force, weight.
W=mg
question
when Fnet = 0 Applying Newton's Laws
answer
constnat speed or stationary
if fnet=0
total Fx=0
total Fy=0
equilibrium when net force=0; static or dynamic
if net force=0, all forces in the x and y direction = 0
question
when Fnet does not equal zero Applying Newton's Laws
answer
accelerating
total Fx=m(ay)
total Fy=m (ax)
NOT at equilibrium
question
A car with a mass of 1500 kg is being towed at a steady speed by a rope held at a 20° angle from the horizontal. A friction force of 320 N opposes the car's motion. What is the tension in the rope?
answer
2 methods
question
•At the first plateau, the jumper is standing still. Draw a FBD for the jumper and determine the jumper's weight and his mass.
•
•
•At the second plateau, the jumper is accelerating upwards. Draw an FBD and determine the net force acting on the jumper. Hint: It is not 2000 N.
•
•Determine the jumper's acceleration.
•
•Determine the jumper's speed as he leaves the ground. Let's assume that he accelerates for 0.25 s.
•
•Determine the jumper's maximum height.
answer
-at first plateau, standing still-FBD
N and W n=weight=1000N
weight=mg 1000N=m(10N/kg) m-100kg
at second plateau: N is largeer than weight (2000N vs. 1000N) Fnet=2000-1000=1000N up
acceleration: 1000N=a(100kg) a=10m/s^2
accelerates for 0.25sec: speed/velocity as leaves ground: change in V=(10m/s^2)(0.25s)= 2.5m/s
starts from 0, so Vf=2.5m/s
max height: at top of jump Vf=0 vi=2.5m/s
0^2 - 2.5^2 = 2 (-9.8m/s^2)(change in y)
change in y= 0.319m
question
in order to jump, must push off floor
if you push off floor then the floor pushes back
answer
to get N force bigger than W force for acceleration in upward direction
question
Example 5.8 Anjay's mass is 70 kg. He is standing on a scale in an elevator and is moving at 5.0 m/s. As the elevator slows to a stop, the scale reads 750 N. Before it stopped, was the elevator moving up or down?
Hint: Draw a FBD. The scale reading is the normal force exerted by the floor of the elevator on Anjay.
answer
nscale on A is 750N
WEonA is 700N
was going up, but elevator slowed down to a stop, so a is positive but velocity is neg
apply newton's second law
question
astronaut bones in space
answer
do not have the weight force compressing the bone
question
Apparent Weight
answer
Your sensation of weight is due to the contact forces supporting you. In most situations we call this supporting force the normal force. However, when we are concentrating on a human and what they are "feeling", we frequently refer to this as the apparent weight.
To find the apparent weight of somebody in an elevator, draw a FBD and then apply Newton's second law.
question
Normal force for Objects on Inclines
answer
ignore friction
rotate picture
normal points up along y axis and w points out at an angle
components: WII to interface is y component
Wperp to interface is x componenet
acceleration perpendicular to the interface has to equal zero
n=mgcos(theta)
if on incline, normal force is smaller than on flat ground
cos(theta < 1
question
5.6 tension on a rope while towing a car: it is accelerating
car with mass= 1500kg towed by a rope at 20 degree angle from the horizontal
friction force is 320N opposes car's motion
what is th etnesion in the rope of the car goes from rest to 12m/s in 10 sec
answer
acceleration is (12m/s)(10s)= 1.2 m/s^2
break T into components Ty=Tsin20
Tx=Tcos20
x direction: accelerating so Tx>320N
in y direction: not accelerating=0
ax=1.2m/s^2
total Fx=m(ax)
m(ax)=Tcos(20)-320
(1500kg)(1.2m/s^2)=Tcos(20)-320
T=2256.06N
question
A box is being pulled to the right at steady speed by a rope that angles upward. In this situation:
A. n > mg
B. n = mg
C. n < mg
D. n = 0
E. Not enough information to judge the size of the normal force
answer
C. n < mg
b/c
n+T=mg (the weight)
question
The box is sitting on the floor of an elevator. The elevator is accelerating upward. The magnitude of the normal force on the box is
answer
A. n > mg
normal force comes from something physically underneath the object
question
An 800-N bicyclist is accelerating up a hill. In this situation
w= 800N
incline is 20 degrees
answer
n=mgcos(theta)
cos(theta) cannot be >1
on flat surface, cos(0)=1, so n=mg
n
question
static friction
If the box is stationary, then ???F ?=0?. There must be a second horizontal force exerted on the box so that ???F ?=0?. What is that force? What is its magnitude and what is its direction?
answer
Friction that acts on objects that are not moving
A force is applied to the box, but the box remains stationary. If the box is stationary, then ???F ?=0?. There must be a second horizontal force exerted on the box so that ???F ?=0?. What is that force? What is its magnitude and what is its direction?
Fnet is 0
question
maximum static friction force
answer
the maximum friction force measured just before the impending motion of an object
A system can only supply a certain amount of static friction. This is called the maximum static friction, fs,max. If the magnitude of the force F is larger than the magnitude of the maximum static friction for the system, the box will begin to slide.
The maximum static friction amount for a system can only be determined by experimental investigation. (empirically).
f_(s,max)= ?_s n
question
f_(s,max)= ?_s n
µs
n
answer
µs is called the coefficient of friction and is found in a table.
n is the magnitude of the normal force. Remember it may or may not be equal to mg.
question
kinetic friction
answer
Friction between moving surfaces
Kinetic friction arises when two surfaces are sliding past each other.
Kinetic friction depends on the materials of the two surfaces and must be determined empirically (meaning--in the lab).
f_k= ?_k n
question
f_k= ?_k n
answer
µk is called the coefficient of kinetic friction. It must be looked up in a table.
n is the magnitude of the normal force.Remember it may or may not be equal to mg
question
static friction constant is always ____ than uk
answer
bigger
at max static friction, starts to slide and don't have to push as much to keep moving b/c uk
question
how friction develops
answer
These two surfaces are sliding or trying to slide past each other. The atomic sized protrusions and valley interact with each other.
very few points are actually in contact b/c atomically there are bumps
question
Carol wants to move her 32 kg sofa to a different room in the house. She places "sofa sliders," slippery disks with ?k = 0.08 on the carpet, under the feet of the sofa. She then pushes the sofa at a steady 0.40 m/s across the floor. How much force does she apply to the sofa?
answer
steady means Fcarol on sofa=fk
question
A car with a mass of 1500 kg is being towed at a steady speed by a rope held at a 20° angle from the horizontal. The coefficients of friction are listed below. The tension in
?_s=0.8
?_k=0.6
?_r=0.3
§Draw FBD
§Determine which coefficient of friction applies.
§Write your ?F_x=m a_x
§Write your ?F_y=0
answer
use rolling friction because being pulled
static friction if driven
question
A student pulls with a 100-N horizontal force on a rope attached to a wall. The tension in the rope is
(a)Less than 100 N.
(b)Equal to 100 N.
Greater than 100 N.
answer
equal to 100N
-must cut rope to see internal tension force
question
Two students are pulling on a rope. Each pulls with a 100 N force. The tension in the rope is
(a)Less than 100 N.
(b)Equal to 100 N.
Greater than 100 N.
answer
equal to 100N
question
A rope connects two boxes (1 10kg, 1 20kg). A second rope is attached to the yellow box and maintains a tension of 300 N. The floor is frictionless. Which of the following statements is true? (There may be more than one true statement.)
a.The acceleration of both blocks is the same.
b.The velocity of both blocks is the same.
c.The acceleration of the 20-kg-block is less than that of the 10-kg-block.
d.The velocity of the 20-kg-block is less than that of the 10-kg-block.
e.The acceleration of the 20-kg-block is more than that of the 10-kg-block.
f.The velocity of the 20-kg-block is more than that of the 10-kg-block.
answer
a.The acceleration of both blocks is the same.
b.The velocity of both blocks is the same.
rope does not crumple up and is not elastic
question
A rope connects two boxes(1 10kg, 1 20kg). A second rope is attached to the yellow box and maintains a tension of 300 N. The floor is frictionless.
(a)Determine the acceleration of each block.
Determine the tension in the rope attaching the green box to the yellow box.
answer
acceleration is the same: so circle both boxes, draw FBD with n, t=300N, and w
accerleration = 300N/60kg= 5m/s^2
determine tension in rope: cute off one box: now n, T, and W
ax=fnetx/m=5m/s^2
5=T/20kg T=100N
question
Conservation Laws
Conservation of Linear Momentum
Conservation of Angular Momentum
Conservation of Energy
Conservation of Mass
what does conservation mean?
what is the system?
answer
The word conservation means that the quantity does not change. What we usually mean is that under some set of conditions, the quantity does not change.
System—composed of interacting objects
question
Collisions
answer
short-duration interaction between two objects
The interaction between the foot and the soccer ball is a collision.
question
impusle
answer
Impulse, J, is the area under the curve
question
impulse is also
answer
The F vs t curve is complicated, so we use the concept of average force.
= Fave ?t
question
impulse causes
answer
Impulse causes a change in the motion of an object.
question
The figure shows a force versus time data for the bounce of a ball.
•What is the impulse on (or delivered to) the ball?
•
•What is the average force on the ball?
answer
J=area under curve
=.5(0.008s)(300N) =1.2N
average force: Fave x change in time=J
1.2N/0.008s=Fave Fave=150N
question
when the stick is in contact with the puck, it exerts a force Fave on the puck, causing it to accelerate
answer
Fave only acts for a short time. It is an impulsive force. We want to find out how it changes the velocity of the puck.
We will start analyzing the problem with Newton's second law. As a result of the analysis, we will find a new quantity called momentum.
question
momentum
Impulse and momentum are vector quantities.
answer
initial momentum + impulse= final momentum
change in momentum=impulse
change in momentum=Fave x change in t
question
Rank the objects according to the magnitudes of the momentum, smallest to largest.
answer
mass x velocity= momentum
question
Two 1.0 kg stationary cue balls are struck by cue sticks. The cues exert the forces shown. Which ball has the greater final speed?
answer
same final speed-b/c impulse is the same b/c area is same
question
A 2.0 kg object moving to the right with speed 0.50 m/s experiences the force shown. What are the object's speed and direction after the force ends?
answer
impulse= 2*.5 = 1Ns etc.
question
A light plastic cart and a heavy steel cart are both pushed with the same force for 1.0 s, starting from rest. After the force is removed, the momentum of the light plastic cart is _____ that of the heavy steel cart.
answer
equal to
same impulse b/c same force x sec=same impulse=same momentum
velocity of smaller mass cart will be larger
question
Practical Implications of the Impulse-Momentum Theorem
?p ?= F ?_ave ?t
if the change in momentum occurs over a long time, the hitting force is ____
if the change in momentum occurs over a short time, the hitting force is ___
answer
is small
large
question
being punched moving into force
moving away from force
answer
into: increase force b/c decreasing the collision time
away: decrease force b/c increasing collision time
-impulse delivered in longer amount of time, but same magnitude, so force decreases
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