Dr. Peter R. Conwell
Physics 211, Physics for Scientists and Engineers
10/16/2005
6th Problem Set: Gravity, Projectile Motion, and Forces in 2 Dimensions
6-1)
What Are Gravitational Forces Like?: Whenever an object is dropped from a distance of a
meter or two very near the surface of the Earth it accelerates in a downward direction with a
magnitude of 9.8 m/s2 in a conventional coordinate system. Two students have come up with
different explanations for this phenomenon:
Jennifer argues: “An object tends to move with a velocity that is proportional to the force on it
and when an object falls there must be a gravitational force on it. This gravitational force in the
downward direction gets larger and larger as the object falls and gets closer to the Earth. This
causes the velocity to get larger and larger as the object falls, so the object undergoes a constant
acceleration because the force gets larger at a constant rate as the object falls.”
Heather argues: “An object tends to move with an acceleration that is proportional to the force on
it. Since all falling objects accelerate at a constant rate, there must be a special gravitational
force attracting it toward the center of the Earth that is essentially constant near the surface of the
Earth.”
Do you agree with Jennifer or with Heather? Which argument is invalid? What observations have
you made that would support your opinion?
6-2)
How Does A Ball Rise? Your partner argues the following about a ball that is tossed vertically
upward after it leaves a person’s hand: “At first when the ball is rising it experiences a net upward
force left over from the toss that gets smaller and smaller as the ball rises.” Do you agree with
your partner’s statement? What evidence do you have from your own observations and
experiments to validate or invalidate the various assertions of your partner?
6-3)
What Happens To The Ball At The Top Of Its Path? Your partner argues the following about a
ball that is tossed vertically upward: “At the top of its path the ball stops for a while so its velocity
is zero. Also, the net force on it is zero so its acceleration is also zero.” Do you agree with your
partner’s statement? What evidence do you have from your own observations and experiments to
validate or invalidate the various assertions of your partner?
6-4)
A pea leaves a pea shooter at a speed of 5.4 m/s. It makes an angle of +30 degrees with respect
to the horizontal.
(a)
Calculate the x-component of the pea's initial velocity.
(b)
Calculate the y-component of the pea's initial velocity.
(c)
Write an expression for the pea's velocity, v , using unit vectors for the x-direction and the ydirection.
Caution: You can use a scientific calculator to find these components from the given angle using
degrees, but if you use a spreadsheet you'll have to express the angle in radians to find
components. (It turns out that 30o = 0.52 radians.)
6-5)
In each case sketch the vector and find the magnitude and angle of the motion with respect to the
x-axis of the following bowling balls moving with respect to a certain coordinate system:
(a)
v = (7.53x + 4.96y ) m
s
(b)
v = (5.45 x – 8.52 y ) m
s
Dr. Peter R. Conwell
Physics 211, Physics for Scientists and Engineers
6-6)
10/16/2005
One of the most powerful attributes of science is the ability that scientists develop to generalize
from their observations and then be able to make predictions about observations they have never
made.
a) Suppose you were to roll the ball briskly in the direction shown and then left it alone. Can you
predict what the resulting graph of its two-dimensional motion would look like? Sketch a graph
frame like that shown below and then sketch the predicted motion in your graph. Explain the
basis for your prediction.
(0,0)
Ball starts at 45
deg&rolls freely
on a floor
+x
-y
(b)
If the initial speed of the ball is 3.5 m/s, what is the magnitude of the x-component of velocity,
vox? Is it positive or negative? What is voy? Is it positive or negative?
(c)
Suppose you and your partner could apply constant forces to the ball at right angles to each other
by tapping quickly and repeadedly on the ball. The direction of the applied forces are indicated on
the diagram. You are the first tapper and you apply a force that is twice that of your partner. Can
you predict what the resulting graph of its two-dimensional motion would look like? Sketch a
graph frame like that shown below and then sketch the predicted motion in your graph. Explain
the basis for your prediction.
direction
of second
tapper
+x
(0,0)
direction
of first
tapper
Ball starts at rest
on a floor
-y
(d)
Suppose a rocket ship is thrust from a tower at a constant acceleration that has a magnitude of
about 9.8 m/s2 in the x-direction and allowed to fall freely toward the ground in the y-direction.
Can you predict what the resulting graph of its two-dimensional motion would look like? Sketch
Dr. Peter R. Conwell
Physics 211, Physics for Scientists and Engineers
10/16/2005
a graph frame like that shown below and then sketch the predicted motion in your graph. Explain
the basis for your prediction.
+x
(0,0)
Rocket is
thrust in the
x-direction
and falls
freely in the
y-direction
-y
6-7)
A person shoved out of a window makes just as good a projectile as a golf ball rolling off a table.
Read the murder mystery entitled A Damnable Man that follows. In order to solve the crime you
should read the section on projectile motion in your text carefully and reason out for yourself what
variables might be important in solving the crime. In fact, not all of the information given in the
mystery is relevant and some information is missing. The missing information you can find for
yourself by observation and experiment. Talk with your classmates and try to determine what
measurements might help you solve the crime. The required measurements are not extensive and
only require apparatus you have already used in the lab. You should be prepared to come into the
lab, if needed, to make some measurements. As you consider various possibilities you might find
in useful to put the information you know, or have computed, in a spread sheet.
(a)
Describe the information you think you need in order to solve the case of A Damnable Man.
Justify your choices and describe what, if any, information is missing.
(b)
Find the missing information and/or take needed measurements. Report on it and describe how
you found this information or took these measurements.
(c)
Solve the crime, explaining clearly all equations and calculations.
A Damnable Man
A warm, quiet, humid night in the city -- the traffic has died away and there isn't even a cooling breeze.
There is a busy hotel that is so well built that sounds don't carry through the windows. The hotel has
impressively large rooms. This is obvious from the outside because there is more space between floors and
rooms than normal. The rooms appear to have 14 foot high ceilings, nice plate glass windows that slide open,
and fully two foot-thick floors for ducting and sound insulation. This is the type of hotel that people like to
stay at when someone else is paying the bill.
Outside the hotel, a man is speaking quietly with the doorman, then begins to measure the plush runway
carpet for replacement. He is reeling out the tape between the hotel and the curb when a scream breaks the
quiet. Looking up, he sees a man falling toward him. Stunned, he drops the tape measure and runs for the
safety of the hotel. The doorman stands, horrified, as the man completes his fall with a sickening sound,
ensuring that the carpet must be replaced. At intense times, people can think of the strangest things, and the
carpet-man finds this to be true. All he can think of are the bloodstains left on his tape measure. Even if they
are cleaned off, he doesn't think he can use it again without thinking of tonight. Even measuring with
another will be hard, and 18 feet will be indelibly marked in his memory—that’s where the blood stains are.
The police arrive and quickly conclude that it is not a suicide – among the victim's personal effects, they find
pictures and records that indicate he has been blackmailing four other occupants of the hotel. He also has
Dr. Peter R. Conwell
Physics 211, Physics for Scientists and Engineers
10/16/2005
bruises on his shins where the ledge at the bottom of the tall hotel window would have hit them; he must
have been pushed pretty hard. Adam Able is the dead man's name, as it appears on the driver's license in his
wallet. His license indicates that Adam was 5'11" tall and weighed 160 lb.. He has been blackmailing
Adrianna Myers, a frail widow in Room 356; Steven Caine, a newspaper reporter in Room 852; Mark
Johnson, a body builder in Room 1956; and Stanley Michaels, an actor in Room 2754. All of the suspects
admit they were in their rooms at the time of the murder. Who killed Adam Able? 1
6-8) In the figure below, a 1kg box on a 30° frictionless incline is connected to a 3.0kg box sitting on a
frictionless horizontal surface. A) If the magnitude of F is 2.3N, what is the tension in the connecting cord?
B) Find the largest value that F can have without the cord becoming slack. Assume that the pulley is
frictionless and massless.
G
F
30°
6-9) In the figure below we see a man sitting in a bosun’s chair2. Bosun’s chairs are used on sailboats to
allow a sailor to pull himself/herself up the mast to repair the sails or the rigging. Assume that the pulley
and the rope are massless. The combined mass of the man and the chair is 95kg. A) Draw a free body
diagram of the forces acting on the man. B) With what force magnitude must the man pull on the rope if he
is to rise with a constant velocity, C) with an upward acceleration of 1.3m/s2.
6-10) In the figure below a horizontal force pushes a 100kg crate up a 30° ramp. A) Draw a free body
diagram of the forces acting on the crate. B) What is the magnitude of the force F? C) What is the
magnitude and direction of the force of the ramp on the crate?
G
F
30°
1 This problem was developed by Kevin Laws.
2 Bosun is short for boat-swain. It evolved from middle English and meant boat slave. Now it refers to a petty officer that has charge
of hull maintenance and related work.