In the figure below Atwood’s machine is drawn - two masses  and  hanging over a
massive pulley of rotational inertia  and radius , connected by a massless unstretchable string.
The string rolls on the pulley without slipping.
a) Find the acceleration of the system and the tensions in the string on both sides of the pulley
in terms of in terms of given variables.
b) Why are the rope tensions on two sides of the pulley not the same? Explain it physically.
c) Suppose mass    and the system is released from rest with the masses at equal heights.
When mass  has descended a distance , find the velocity of each mass and the angular
velocity of the pulley.
[4***] A string is rolled around a cylinder(   kg) as shown in figure. A person pulls on the
string, causing the cylinder to roll without slipping along the floor

Transcribed Image Text:a) If there is a tension of 30 N in the string, what is the acceleration of the cylinder? b) What is the direction of static friction as it rolls? c) When the cm of cylinder moved a distance d= 2m, how much work done by the tension? [5**] A uniform stick of mass m and length L is suspended horizontally with end B at the edge of a table and the other end A is held by hand. Point A is suddenly released. At the instant after release: a) What is the torque about the end B on the table? b) What is the angular acceleration about the end B on the table? c) What is the vertical acceleration of the center of mass? d) What is the vertical component of the hinge force at B ? Does the hinge force have a horizontal component at the instant after release? [6**] A cylinder of mass m and radius R rolls without slipping down a rough slope of height H onto an frictionless track at the bottom that leads up a second frictionless hill as shown. a) How fast is the cylinder moving at the bottom of the first incline? How fast is it rotating? b) Does the cylinder's angular velocity it leaves the rough track and moves onto the ice (in the middle of the flat stretch in between the hills)? c) How far up the second hill (vertically, find H ) does the disk go before it stops rising? rough H frietionless [7+] A playground merry-go-round with an axis at the center (radius R = 2.0 m and rotational inertia I = 500 kg.m²) is initially at rest. A girl of mass m = 43 kg is running at speed v. = 3.4 m/s in a direction tangent to the disk of the merry-go-round, intending to jump on to the edge. a) What is the magnitude of the angular velocity of the merry-go-round after the girl has jumped on at the edge? b) Is it possible for her, with the same initial speed, to jump onto the merry-go-round at the same point, but not make it spin? If so, how could she do this?
Transcribed Image Text:an angle e with respect to the horizontal in an isometric curl as shown. The muscle that supports the suspended weight is connected a short distance d up from the elbow joint. The bone that supports the weight has length D. a) Find the tension T in the muscle, assuming for the moment that the center of mass of the forearm is in the middle at D/2. Note that it is much larger than the weight of the arm and barbell combined, assuming a reasonable ratio of D/d = 25 or thereabouts. b) Find the force F (magnitude and direction) exerted on the supporting bone by the elbow joint. Again, note that it is much larger than "just" the weight being supported. M. D [9*] A crate of mass 100 kg rests on a 33' incline. The coefficient of friction between the incline and the crate is µ, = 0.75. There are two ways the block can move: by slipping down the incline or by tipping over. For this problem, use g = 9.8 m/s?. a) Determine the minimum force F to prevent the crate from tipping. b) Determine the minimum force F to prevent the crate from slipping. c) What is the nature of the impending motion for the minimum force F? 1m 1m 2 m COM 1m 330 [10**] A cylinder has a radius R and weight W. You try to roll it over a step of height h < R. The force (F) is applied at the axle of the wheel, at angle 0 above the horizontal. What is the value of 0 for which F is smallest? F

Question

In the figure below Atwood’s machine is drawn - two masses  and  hanging over a
massive pulley of rotational inertia  and radius , connected by a massless unstretchable string.
The string rolls on the pulley without slipping.
a) Find the acceleration of the system and the tensions in the string on both sides of the pulley
in terms of in terms of given variables.
b) Why are the rope tensions on two sides of the pulley not the same? Explain it physically.
c) Suppose mass    and the system is released from rest with the masses at equal heights.
When mass  has descended a distance , find the velocity of each mass and the angular
velocity of the pulley.
[4***] A string is rolled around a cylinder(   kg) as shown in figure. A person pulls on the
string, causing the cylinder to roll without slipping along the floor

a) If there is a tension of 30 N in the string, what is the acceleration of the cylinder?
b) What is the direction of static friction as it rolls?
c) When the cm of cylinder moved a distance d= 2m, how much work done by the tension?
[5**] A uniform stick of mass m and length L is suspended horizontally with end B at the edge
of a table and the other end A is held by hand. Point A is suddenly released. At the instant after
release:
a) What is the torque about the end B on the table?
b) What is the angular acceleration about the end B on the table?
c) What is the vertical acceleration of the center of mass?
d) What is the vertical component of the hinge force at B ? Does the hinge force have a
horizontal component at the instant after release?
[6**] A cylinder of mass m and radius R rolls without slipping down a rough slope of height H
onto an frictionless track at the bottom that leads up a second frictionless hill as shown.
a) How fast is the cylinder moving at the bottom of the first incline? How fast is it rotating?
b) Does the cylinder's angular velocity
it leaves the rough track and moves onto the ice
(in the middle of the flat stretch in between the hills)?
c) How far up the second hill (vertically, find H ) does the disk go before it stops rising?
rough
H
frietionless
[7+] A playground merry-go-round with an axis at the center (radius R = 2.0 m and rotational
inertia I = 500 kg.m²) is initially at rest. A girl of mass m = 43 kg is running at speed v. =
3.4 m/s in a direction tangent to the disk of the merry-go-round, intending to jump on to the
edge.
a) What is the magnitude of the angular velocity of the merry-go-round after the girl has
jumped on at the edge?
b) Is it possible for her, with the same initial speed, to jump onto the merry-go-round at the
same point, but not make it spin? If so, how could she do this?

an angle e with respect to the horizontal in an isometric curl as shown. The muscle that supports
the suspended weight is connected a short distance d up from the elbow joint. The bone that
supports the weight has length D.
a) Find the tension T in the muscle, assuming for the moment that the center of mass of the
forearm is in the middle at D/2. Note that it is much larger than the weight of the arm and
barbell combined, assuming a reasonable ratio of D/d = 25 or thereabouts.
b) Find the force F (magnitude and direction) exerted on the supporting bone by the elbow joint.
Again, note that it is much larger than "just" the weight being supported.
M.
D
[9*] A crate of mass 100 kg rests on a 33' incline. The coefficient of friction between the incline
and the crate is µ, = 0.75. There are two ways the block can move: by slipping down the incline
or by tipping over. For this problem, use g = 9.8 m/s?.
a) Determine the minimum force F to prevent the crate from tipping.
b) Determine the minimum force F to prevent the crate from slipping.
c) What is the nature of the impending motion for the minimum force F?
1m
1m
2 m
COM
1m
330
[10**] A cylinder has a radius R and weight W. You try to roll it over a step of height h < R.
The force (F) is applied at the axle of the wheel, at angle 0 above the horizontal. What is the
value of 0 for which F is smallest?
F

Accepted Answer

We can use the second equation of motion expression for the acceleration in terms of net.The torque…

4***] A string is rolled around a cylinder(   kg) as shown in figure. A person pulls on the string, causing the cylinder to roll without slipping along the floor