Download Ch6 Homework – Physics I

Ch5 Homework – Physics I
For EVERY problem you must include a written statement about how reasonable your
answer is. Consider whether you have the correct units, correct algebraic sign, and
whether or not the answer makes physical sense. You do NOT need to do this for
conceptual questions.
CH5A:
C.1
Can an object move if there is no net force on it? Explain.
C.2
Suppose you apply a force of 1 N to block A and a force of 2 N to block B. Does it
follow that block B has twice the acceleration of block A? Justify your answer using Newton's
second law.
C.3
When a brick rests on a flat, stationary, horizontal table, there is an upward normal force
on it from the table. Explain why the brick does not accelerate upward in response to this force.
0.1
Use the simulation in the interactive problem in this section to answer the following
question. If the net force on the helicopter is zero, what must the helicopter be doing?
2.1
An airplane of mass 2867 kg flies at a constant horizontal velocity. The force of air
resistance on it is 2225 N. What is the net force on the plane (magnitude and direction)?
2.2
Three children are pulling on a toy that has a mass of 1.25 kg. Child A pulls with force
(5.00, 6.00, 2.50) N. Child B pulls with force (0.00, 9.20, 2.40) N. With what force must Child C
pull for the toy to remain stationary?
--------------------------------------------------------------------------------------------------Ch5B:
C.4
A rocket in space can change course with its engines. Since in empty space there is
nothing for the exhaust gases to push on, how can it accelerate?
C.5
Blocks 1 and 2, and 2 and 3 are connected by two identical thin wires. All three blocks
are resting on a frictionless table. Block 1 is pulled by a constant force and all three blocks
accelerate equally in a line, with block 1 leading. Are the tensions in the two wires the same or
different? If the tensions are different, which has the larger magnitude? Why?
C.6
Two blocks of different mass are connected by a massless rope which goes over a
massless, frictionless pulley. The rope is free to move, and both of the blocks hang vertically.
What is the magnitude of the tension in the rope?
4.1
A weightlifter can exert an upward force of 3750 N. If a dumbbell has a mass of 225 kg,
what is the maximum number of dumbbells this weightlifter could hold simultaneously if he
were on the Moon? (The Moon's acceleration due to gravity is approximately 0.166 times freefall
acceleration on Earth.) The weightlifter cannot pick up a fraction of a dumbbell, so make sure
your answer is an integer number of dumbbells
4.2
(a) How much does a 70.0 kg person weigh on the Earth? (b) How much would she
weigh on the Moon (gmoon = 0.166g)? (c) How much would she weigh on a neutron star where
gstar = 1.43×1011g?
4.3
A dog weighs 47.0 pounds on Earth. (a) What is its weight in newtons? (One newton
equals 0.225 pounds.) (b) What is its mass in kilograms?
Ch5C:
5.1
When empty, a particular helicopter of mass 3770 kg can accelerate straight upward at a
maximum acceleration of 1.34 m/s2. A careless crewman overloads the helicopter so that it is
just unable to lift off. What is the mass of the cargo?
5.5
A flea has a mass of 4.9×10-7 kg. When a flea jumps, its rear legs act like catapults,
accelerating it at 2400 m/s2. What force do the flea's legs have to exert on the ground for a flea
to accelerate at this rate?
5.11 There are two forces acting on a box of golf balls, F1 and F2. The mass of the box is 0.750
kg. When the forces act in the same direction, they cause an acceleration of 0.450 m/s2. When
they oppose one another, the box accelerates at 0.240 m/s2 in the direction of F2. (a) What is the
magnitude of F1? (b) What is the magnitude of F2?
5.9
A solar sail is used to propel a spacecraft. It uses the pressure (force per unit area) of
sunlight instead of wind. Assume the sail and its spacecraft have a mass of 245 kg. If the sail has
an area of 62,500 m2 and achieves a velocity of 8.93 m/s in 12.0 hours starting from rest, what
pressure does light of the Sun exert on the sail? To simplify the problem, ignore other forces
acting on the spacecraft and assume the pressure is constant even as its distance from the Sun
increases.
5.13 Cedar Point's Top Thrill Dragster Strata-Coaster in Ohio, the fastest amusement park ride in
the world as of 2004, can accelerate its riders from rest to 193 km/h in 4.00 seconds. (a) What is
the magnitude of the average acceleration of a rider? (b) What is the average net force on a 45.0
kg rider during these 4.00 seconds? (c) Do people really pay money for this?
5.15 A 7.6 kg chair is pushed across a frictionless floor with a force of 42 N that is applied at
an angle of 22° downward from the horizontal. What is the magnitude of the acceleration of the
chair?
Ch5 Homework – Physics I
For EVERY problem you must include a written statement about how reasonable your
answer is. Consider whether you have the correct units, correct algebraic sign, and
whether or not the answer makes physical sense. You do NOT need to do this for
conceptual questions. EVERY problem must ALSO have a FBD for it.
Ch5D:
10.1 A 75.0 kg man sits on a massless cart that is on a horizontal surface. The cart is initially
stationary and it can move without friction or air resistance. The man throws a 5.00 kg stone in
the positive direction, applying a force to it so that it has acceleration +3.50 m/s2 as measured by
a nearby observer on the ground. What is the man's acceleration during the throw, as seen by the
same observer? Be careful to use correct signs. (You must draw FBD’s for both the man and the
stone AS HE’S THROWING IT.)
11.2 Three blocks are arranged in a stack on a frictionless horizontal surface. The bottom block
has a mass of 37.0 kg. A block of mass 18.0 kg sits on top of it and a 16.0 kg block sits on top of
the middle block. A downward vertical force of 170 N is applied to the top block. What is the
magnitude of the normal force exerted by the bottom block on the middle block? (Draw a FBD
for the middle block.)
11.3 A 22.0 kg child slides down a slide that makes a 37.0° angle with the horizontal. (a) What
is the magnitude of the normal force that the slide exerts on the child? (b) At what angle from the
horizontal is this force directed? State your answer as a number between 0 and 90°. (Draw a
FBD for the child.)
11.4 A 6.00 kg box is resting on a table. You push down on the box with a force of 8.00 N.
What is the magnitude of the normal force of the table on the block? (Draw a FDB for the box.)
12.2 During recess, Maria, who has mass 27.0 kg, hangs motionless on the monkey bars, with
both hands gripping a horizontal bar. Assume her arms are vertical and evenly support her body.
What is the tension in each of her arms? (Draw a FBD for Maria.)
12.3 Mr. Hood’s Special: Maria now moves her hands apart such that her left arm forms a 10º
angle from vertical while her right makes a 35º angle from vertical. What is the tension in each
arm? She is still holding herself stationary. (Draw a FBD for Maria.)
Ch5E:
C.7
Why is the frictional force proportional to the normal force, and not weight?
C.8
A college rower can easily push a small car along a flat road, but she cannot lift the car in
the air. Since the mass of the car is constant, how can you explain this discrepancy?
C.9
Without friction, you would not be able to walk along a level sidewalk. Why? (Imagine
being stranded in the middle of an ice rink, wearing shoes made of ice.)
19.1 A piece of steel is held firmly in the jaws of a vise. A force larger than 3350 N will cause
the piece of steel to start to move out of the vise. If the coefficient of friction between the steel
and each of the jaws of the vise is 0.825 and each jaw applies an equal force, what is the
magnitude of the normal force exerted on the steel by each jaw?
20.1 A 1.5 kg brick is pushed against a vertical wall by a horizontal force. If µs = 0.4 what is
the minimum force necessary to keep the block from sliding down the wall?
20.4 An old car is traveling down a long, straight, dry road at 25.0 m/s when the driver slams
on the brakes, locking the wheels. The car comes to a complete stop after sliding 215 m in a
straight line. If the car has a mass of 755 kg, what is the coefficient of kinetic friction between
the tires and the road? Describe what you think the weather and road conditions were like based
on this value.
20.5 A rescue worker pulls an injured skier lying on a toboggan (with a combined mass of 127
kg) across flat snow at a constant speed. A 2.43 m rope is attached to the toboggan at ground
level, and the rescuer holds the rope taut at shoulder level. If the rescuer's shoulders are 1.65 m
above the ground, and the tension in the rope is 148 N, what is the coefficient of kinetic friction
between the toboggan and the snow?
Ch5F:
C.12 One end of a spring is attached firmly to a wall, and a block is attached to the other end.
When the spring is fully compressed, it exerts a force F on the block, and when the spring is fully
extended, the force it exerts on the block is -F. What is the force of the spring on the block at (a)
equilibrium (neither compressed nor stretched), (b) halfway between maximum stretch and
equilibrium, and (c) halfway between maximum compression and equilibrium? Carefully
consider the signs in your answer, which indicate direction, and express your answers in terms of
28.1 A 10.0 kg mass is placed on a frictionless, horizontal surface. The mass is connected to
the end of a horizontal compressed spring which has a spring constant 339 N/m. When the spring
is released, the mass has an initial, positive acceleration of 10.2 m/s2. What was the displacement
of the spring, as measured from equilibrium, before the block was released? Watch the sign of
your answer.
28.2 Consider a large spring, hanging vertically, with spring constant k = 3220 N/m. If the
spring is stretched 25.0 cm from equilibrium and a block is attached to the end, the block stays
still, neither accelerating upward nor downward. What is the mass of the block?
28.3 A spring with spring constant k = 15.0 N/m hangs vertically from the ceiling. A 1.20 kg
mass is attached to the bottom end of the spring, and allowed to hang freely until it becomes
stationary. Then, the mass is pulled downward 10.0 cm from its resting position and released. At
the moment of its release, what is (a) the magnitude of the mass's acceleration and (b) the
direction? Ignore the mass of the spring.
28.4 A 5.00 kg wood cube rests on a frictionless horizontal table. It has two springs attached to
it on opposite faces. The spring on the left has a spring constant of 55.0 N/m, and the spring on
the right has a spring constant of 111 N/m. Both springs are initially in their equilibrium
positions (neither compressed nor stretched). The block is moved toward the left 10.0 cm,
compressing the left spring and stretching the right spring. (a) Calculate the resulting net force on
the block. (b) Calculate the initial acceleration of the block when it is released. Use the
convention that to the right is positive and to the left is negative.
28.5 A man steps on his bathroom scale and obtains a reading of 243 lb. The spring in the
scale is compressed by a displacement of -0.0590 inches. Calculate the value of its spring
constant in (a) pounds per inch (b) newtons per meter.
Ch5G:
C.1 Only one non-zero force acts on an object. Can the object be and remain at rest? Explain.
C.2
If an object has no velocity, does that necessarily mean no forces are acting on it?
Explain your answer.
C.3
A massless rope is hanging over a massless and frictionless pulley. A large bunch of
bananas is tied to one end of the rope, and a monkey of equal weight is clinging to the other end,
at a lower height. The monkey decides he wants the bananas and starts to climb his side of the
rope. What happens to the bananas as the monkey climbs? Why?
C.4
A car is parked on a downhill section of a hill. What forces are acting on the car?
Answer using a FBD with labels.
C.5
Imagine using a spring scale on the Moon, where the acceleration of gravity is less than
on Earth. Would the scale display different values on the Moon and Earth? Explain.
9.3
At a construction site, two barrels, each of mass of 122 kg, are connected by a long,
massless rope that passes over an ideal pulley that is mounted high overhead. The red barrel is at
ground level, and the blue barrel is 8.26 m off the ground, at the third story of a building. Some
careless bricklayers hold the blue barrel in place, load it with 200 kg of bricks, and then let it
drop. (a) Calculate the maximum speed of the red barrel. (b) What is the maximum height that
the red barrel reaches? Remember that it is still moving upward even after the blue barrel hits the
ground and stops.