Rolling ball on a ramp

1
Rolling ball on a ramp

• How would you describe the motion of the ball
  rolling on this ramp if you could not share the
  image of the ramp?

• What is the acceleration at E?
• 1. 2. 3. 4.
• What is the acceleration at C?
• 1. 2. 3. 4.

2
Playing catch on Exidor

• A physics student on Planet Exidor throws a ball
  that follows the parabolic trajectory shown. The
  balls position is shown at one-second intervals
  until t 3 s. At t 1 s, the balls velocity
  is

The balls velocity at t 0 s is a.
b. c. d.
2
1
3
0

• Uniformly accelerated motion means constant
  velocity change

3
Battleship!

• A
• Both at same time
• B
• Need more information

A
B

• A battleship simultaneously launches two shells
  at enemy ships. If the shells follow the
  trajectories shown, which ship gets hit first?

4
Rocket science

• A rocket of mass m launches at and maintains an
  angle of 45 above the ground. The thrust force
  is Fthrust, and it is assumed that the mass and
  thrust remain unchanged.

• What is the trajectory of the rocket?
• Assume the case of no gravity

• Arc curving up
• Straight line
• Arc curving down

Fthrust
45
5
Rocket science

• A rocket of mass m launches at and maintains an
  angle of 45 above the ground. The thrust force
  is Fthrust, and it is assumed that the mass and
  thrust remain unchanged.

• What is the trajectory of the rocket?
• Now apply gravity

• Arc curving up
• Straight line
• Arc curving down

Fthrust
45
w
6
Baggage exclaim

• Tired of carrying your luggage through the tunnel
  at Hartsfield-Jackson airport, you decide to drop
  your 10 kg bag on the moving walk next to you and
  pick it up at the end of the walk 12 m away. You
  match speed with the walk (0.75 m/s) and drop
  your bag straight down. A person 20 m behind
  you, who is strolling on the walk at 1.25 m/s,
  sees you do this and complains, declaring that
  you will both be at the end of the walk at the
  same time. Is the other traveler correct?

• What is Vx?
• 2.0 m/s
• 1.25 m/s
• 0.75 m/s
• 0.5 ms/

12 m
20 m
7
Baggage exclaim

• Tired of carrying your luggage through the tunnel
  at Hartsfield-Jackson airport, you decide to drop
  your 10 kg bag on the moving walk next to you and
  pick it up at the end of the walk 12 m away. You
  match speed with the walk (0.75 m/s) and drop
  your bag straight down. A person 20 m behind
  you, who is strolling on the walk at 1.25 m/s,
  sees you do this and complains, declaring that
  you will both be at the end of the walk at the
  same time. Is the other traveler correct?

• What is t in the figure?
• Cant tell
• t lt 0
• t 0
• t gt 0

12 m
20 m
8
Baggage exclaim

• Tired of carrying your luggage through the tunnel
  at Hartsfield-Jackson airport, you decide to drop
  your 10 kg bag on the moving walk next to you and
  pick it up at the end of the walk 12 m away. You
  stand next to the walk (moving at 0.75 m/s) and
  drop your bag straight down. How far does your
  bag slide before it moves with the walk if the
  coefficients of friction are ?s 0.05 and ?k
  0.05?

• Select the appropriate free-body diagram

Fwalk
Fwalk
1
2
3
9
Dark brown is the river

• A boat takes 5.0 hours to travel 30 km up a
  river, then 3.0 hours to return. How fast is the
  river flowing?

• In which reference frame is the boats speed
  measured?

The boat is not moving with respect to itself!
V
3. boat
10
Dark brown is the river

• A boat takes 5.0 hours to travel 30 km up a
  river, then 3.0 hours to return. How fast is the
  river flowing?

• In which reference frame is the boats speed
  measured?

The boat is not moving with respect to itself!
V
11
Dark brown is the river

• A boat takes 5.0 hours to travel 30 km up a
  river, then 3.0 hours to return. How fast is the
  river flowing?

• What is the boats groundspeed as it goes
  upstream?

• 2 km/h
• 4 km/h
• 6 km/h
• 7.5 km/h
• 10 km/h

V
Distance is measured with respect to the ground.
12
Dark brown is the river

• A boat takes 5.0 hours to travel 30 km up a
  river, then 3.0 hours to return. How fast is the
  river flowing?

• What is the boats groundspeed heading downstream?

What is the average velocity of the boat?

• 2 km/h
• 4 km/h
• 6 km/h
• 7.5 km/h
• 10 km/h

V
What is the average speed of the boat?
13
Dark brown is the river

• A boat takes 5.0 hours to travel 30 km up a
  river, then 3.0 hours to return. How fast is the
  river flowing?

• vu v V
• vd v V
• vu vd v - v 2V
• 6 - 10 -2V
• V 2 km/h

• 2 km/h
• 4 km/h
• 6 km/h
• 7.5 km/h
• 10 km/h

V
14
Oldies kinematics

• Vinyl records, i.e., LP, 45, 78, are classified
  by rpm, the number of revolutions per minute.

• Recall that the LP turns at 33.3 rpm.
• Which is true?

In one minute, An LP spins 33 times, a 45 spins
45 times, and a 78 spins 78 times.

• T78 gt T45 gt TLP
• T78 lt T45 lt TLP
• TLP gt T78 gt T45
• TLP lt T78 lt T45

1 revolution
15
Block on a rope

• What forces act on the block?

• Weight, normal force, tension, centripetal force,
  static friction
• Weight, normal force, tension, centripetal force,
  kinetic friction
• Weight, normal force, tension, kinetic friction

16
Marble in a hoop

• The instantaneous velocity at any point in a
  circular orbit will be tangent to the circle.

3
2
4
1
5

• Which vector represents the instantaneous
  velocity of the ball at the point shown?

17
5
4
6
3
2
1

• In the absence of a net force, the velocity of
  the marble will not change after it leaves the
  hoop.

• If the hoop is suddenly cut, as shown, which
  vector best represents the subsequent path of the
  marble?

18
Block on a turntable
z
x-y
n
1
fs
w
fs
n

• What forces act on the block at the position
  shown?

2
w
n

• Friction constrains the block to follow a
  circular path.

3
fs
w
19
Block on a turntable

• Which path best describes the motion of the block
  after it begins to slide?

2
3
4

• Once ? is too big, static friction cannot
  constrain the block to a circular path.
• Kinetic friction will divert the path from a
  straight line.

?
1
20
Vertical circular motion

• Where is the apparent weight the greatest?

v
n
g
1

• At this point
• wapp gt w
• wapp w
• wapp lt w

v
n
n
2
3
g
g
4
v
v
n
g
21
Catch!

• Consider two people on the opposite sides of a
  rotating merry-go-round. One of them throws a
  ball toward the other. In which frame of
  reference is the path of the ball straight when
  viewed from above
• the frame of reference of the merry-go-round, or
• that of the earth?

• (a) only
• (a) and (b) - although the path appears to curve
• (b) only
• Neither because its thrown while in circular
  motion, the ball travels along a curved path.

The path is straight in an inertial reference
frame
?
22
Action/reaction pairs

• A thrust force from its propeller pulls a plane
  forward
• a drag force pushes it backward.

• Is the thrust/drag pair a Third law pair?
• Yes
• No
• Yes, if the plane is flying at a constant
  velocity
• Cannot tell from given information

Third law pairs act on different objects!
23
Newtons Laws

• A thrust force from its propeller pulls a plane
  forward
• a drag force pushes it backward.

• Which of Newtons Laws relates these pairs as the
  plane takes off?
• First Law only
• Second Law only
• First Law or Second Law
• Third Law

24
Action/reaction pairs

• A car exerts a forward force on a trailer
• the trailer tugs backward at the car.

• Is the car pulling/trailer tugging a Third law
  pair?
• Yes
• No
• Yes, but only when the car and trailer move at a
  constant velocity
• Cannot tell from given information

25
Action/reaction pairs

• A motorboat propeller pushes backward on the
  water
• the water pushes forward on the propeller.

• Is the propeller pushing/water pushing a Third
  law pair?
• Yes
• No
• Yes, but only when the boat moves at a constant
  velocity
• No, water cannot push
• Cannot tell from given information

This is the means of the boats propulsion.
26
Action/reaction pairs

• Gravity pulls down on a person sitting in a
  chair
• The chair pushes back up on the person.

• Is gravity pulling/chair pushing a Third law
  pair?
• Yes
• No
• Cannot tell from given information

Third law pairs result from the same interaction!
27
Action/reaction pairs

• Gravity pulls down on a person sitting in a
  chair
• The chair pushes back up on the person.

• Which of Newtons Laws relates these pairs?
• First Law only
• Second Law only
• First Law or Second Law
• Third Law

28

• A ball of mass m on a string of length r is swung
  in a vertical circle about a point h above the
  floor. The tension in the string when the ball
  is at the very bottom of the circle is T. A very
  sharp knife is suddenly inserted, as shown.

• Which path best describes the trajectory of the
  ball after the string is cut?
• Path A
• Path B
• Path C
• Path D

A
B
C
D
29
Tense situation
?
2
A
B
m

• Compare the tension at the point at which the
  string is attached to the wall in A with the
  tension in the middle of the string in B.

• TA 2TB
• TA TB
• TB (1/2)TA
• TB (1/4)TA

30
With a cord
A

• Block A, supported by a frictionless table, is
  connected via a massless string and massless,
  frictionless pulley to block B, which is hanging
  over the edge of the table.
• Initially, block A was held in place by someones
  hand. How is the tension in the string before
  release related to the tension after release?

B

• Tbefore Tafter
• Tbefore gt Tafter
• Tbefore lt Tafter

31
Ties that bind
F

• Two 1.0 kg blocks are connected by a rope. A
  second rope hangs beneath the lower block. Both
  ropes have a mass of 250 g. A force, F,
  accelerates the entire assembly up at 3.0 m/s2.
  What is F?

A
B

• 7.5 N
• 25 N
• 26 N
• 32 N

32

• A locomotive pulling a train is accelerating the
  train on a level track. The tension in the
  couplings is

• the same anywhere along the train.
• least between the locomotive and the first car.
• least between the last car and the caboose.
• none of the above.