1) A solid ball of mass M and radius R rolls without slipping down a hill...
1) A solid ball of mass M and radius R rolls without slipping down a hill with slope tan θ. (That is θ is the angle of the hill relative to the horizontal direction.)
What is the static frictional force acting on it? It is possible to solve this question in a fairly simple way using two ingredients:
a) As derived in the worksheet when an object of moment of inertia I, mass M and radius R starts at rest at the top of a constant slope, then rolls without slipping to the bottom, which is lower by a distance h, the speed at the bottom is given by (1/2)Mv2[1+I/(MR2)]=Mgh.
b) The center of mass of the ball has the same motion as a point particle acted on by the external forces: gravity, the normal force and the static friction force. 2) If the coefficient of static friction is μs=.3, what is the maximum slope (given by the value of θ) down which the solid ball can roll without slipping?
Homework Answers
Add Answer to:
1) A solid ball of mass M and radius R rolls without slipping
down a hill...
A solid ball of mass 2.0 kg rolls down a hill of slope 38 degree without...
A solid ball of mass 2.0 kg rolls down a hill of slope 38 degree without slipping. Find the acceleration of the ball’s center of mass, the frictional force between ball and ground, and the minimum coefficient of static friction needed to prevent slipping.
A solid cylinder of radius R and mass m, and moment of inertia mR2/2, starts from rest and rolls down a hill without slipping.
A solid cylinder of radius R and mass m, and moment of inertia mR2/2, starts from rest and rolls down a hill without slipping. At the bottom of the hill, the speed of the center of mass is 4.7 m/sec. A hollow cylinder (moment of inertia mR2) with the same mass and same radius also rolls down the same hill starting from rest. What is the speed of the center of mass of the hollow cylinder at the bottom of...
Problem 4. A solid sphere of mass m and radius r rolls without slipping along the...
Problem 4. A solid sphere of mass m and radius r rolls without slipping along the track shown below. It starts from rest with the lowest point of the sphere at height h 3R above the bottom of the loop of radius R, much larger than r. Point P is on the track and it is R above the bottom of the loop. The moment of inertia of the ball about an axis through its center is I-2/S mr. The...
A circular hoop of mass m, radius r, and infinitesimal thickness rolls without slipping down a ramp inclined at an angle θ with the horizontal. (Intro 1figure)
A circular hoop of mass m, radius r, and
infinitesimal thickness rolls without slipping down a ramp inclined at an angle θ with the
horizontal. (Intro 1figure)part a)What is the acceleration of
the center of the hoop?Express the acceleration in terms of physical constants and all or some of the
quantities m,r,and θ.part b)What is the minimum coefficient of
(static)friction needed
for the hoop to roll without slipping? Note that it is static and
not kinetic friction that is relevant here,...
2) A solid uniform ball of mass m and radius r rolls down a hemispherical bowl...
2) A solid uniform ball of mass m and radius r rolls down a hemispherical bowl of radius R, starting from a height h above the bottom of the bowl. The surface on the left half of the bowl has sufficient friction to prevent slipping, and the right side is frictionless. R (a) (5 marks) Determine the angular speed w the ball rotates in terms of e', when it rolls without slipping. (b) (5 marks) Derive an expression for the...
A solid sphere of uniform density starts from rest and rolls without slipping down an inclined...
A solid sphere of uniform density starts from rest and rolls
without slipping down an inclined plane with angle θ =
30o. The sphere has mass M = 8
kg and radius R = 0.19 m . The
coefficient of static friction between the sphere and the plane is
μ = 0.64. What is the magnitude of the frictional
force on the sphere?
Ff =
N
Problem 9 m,r A solid ball of mass m and radius r sits at rest at the top of a hill of height H l...
Problem 9 m,r A solid ball of mass m and radius r sits at rest at the top of a hill of height H leading to a circular loop-the loop. The center of mass of the ball will move in a circle of radius R if it goes around the loop. The moment of inertia of a solid ball is Ibull--mr. (a) Find an expression for the minimum height H for which the ball barely goes around the loop, staying...
A solid disk (radius R=2.5 cm , mass M =0.35 kg) rolls without slipping down an...
A solid disk (radius R=2.5 cm , mass M =0.35 kg) rolls without slipping down an 30 degree-incline. If the incline is 4.2 m long and the disk starts from rest, what is the linear velocity of its center of mass at the bottom of the incline (in m/s)?
A solid 0.4750-kg ball rolls without slipping down a track toward a loop-the-loop of radius R-...
A solid 0.4750-kg ball rolls without slipping down a track toward a loop-the-loop of radius R- 0.7150 m. What minimum translational speed Vmin must the ball have wher it is a height H- 1.062 m above the bottom of the loop, in order to complete the loop without falling off the track'? Number "min0.294 m/s figure not to scale
A solid sphere of mass M and radius R sits on a an incline of angle...
A solid sphere of mass M and radius R sits on a an incline of angle θ, when it is let go it rolls down-hill without slipping at total vertical distance of h. At the bottom of the hill the ball moves onto a horizontal surface and enters into a completely elastic collision with a stationary block of height 2R and mass 2M. Find the speed of the block right after the collision.
Problem 4. A solid sphere of mass m and radius r rolls without slipping along the track shown below. It starts from rest with the lowest point of the sphere at height h 3R above the bottom of the loop of radius R, much larger than r. Point P is on the track and it is R above the bottom of the loop. The moment of inertia of the ball about an axis through its center is I-2/S mr. The...
A circular hoop of mass m, radius r, and
infinitesimal thickness rolls without slipping down a ramp inclined at an angle θ with the
horizontal. (Intro 1figure)part a)What is the acceleration of
the center of the hoop?Express the acceleration in terms of physical constants and all or some of the
quantities m,r,and θ.part b)What is the minimum coefficient of
(static)friction needed
for the hoop to roll without slipping? Note that it is static and
not kinetic friction that is relevant here,...
2) A solid uniform ball of mass m and radius r rolls down a hemispherical bowl of radius R, starting from a height h above the bottom of the bowl. The surface on the left half of the bowl has sufficient friction to prevent slipping, and the right side is frictionless. R (a) (5 marks) Determine the angular speed w the ball rotates in terms of e', when it rolls without slipping. (b) (5 marks) Derive an expression for the...
A solid sphere of uniform density starts from rest and rolls
without slipping down an inclined plane with angle θ =
30o. The sphere has mass M = 8
kg and radius R = 0.19 m . The
coefficient of static friction between the sphere and the plane is
μ = 0.64. What is the magnitude of the frictional
force on the sphere?
Ff =
N
Problem 9 m,r A solid ball of mass m and radius r sits at rest at the top of a hill of height H leading to a circular loop-the loop. The center of mass of the ball will move in a circle of radius R if it goes around the loop. The moment of inertia of a solid ball is Ibull--mr. (a) Find an expression for the minimum height H for which the ball barely goes around the loop, staying...
A solid 0.4750-kg ball rolls without slipping down a track toward a loop-the-loop of radius R- 0.7150 m. What minimum translational speed Vmin must the ball have wher it is a height H- 1.062 m above the bottom of the loop, in order to complete the loop without falling off the track'? Number "min0.294 m/s figure not to scale
Most questions answered within 3 hours.
-
Consider the reaction, C3 H8 + O2 --> CO2 + H2O. How many
moles of O2...
asked 21 minutes ago -
You and your opponent both roll a fair die. If you both roll the
same number,...
asked 39 minutes ago -
In a study of the accuracy of fast food drive-through orders,
Restaurant A had 257 accurate...
asked 38 minutes ago -
Identify and describe in detail the four categories of
institutions that could be included in a...
asked 44 minutes ago -
In python
class Customer:
def __init__(self, customer_id, last_name, first_name, phone_number, address):
self._customer_id = int(customer_id)
self._last_name =...
asked 52 minutes ago -
What is an example of a limitation in implementing a new
ERP system and how it...
asked 47 minutes ago -
In a section of 9.7cm of an artery with a radius of 2.6mm there
is a...
asked 48 minutes ago -
the two carboxylic acid groups of aspartic acid have different
acidities with pKa values of 2.1...
asked 52 minutes ago -
Would CuCO3 aqueous salt combined with calcium chloride
form a solid precipitate? If so, what would...
asked 51 minutes ago -
How do ECM Solutions assist in embedding a culture of continuous
improvement in an organization? (Project...
asked 1 hour ago -
Directions
These directions introduce the idea of Essential Questions.
Since this may be a new concept...
asked 1 hour ago -
1.b. Fiscal policy is said to suffer from ‘crowding out’.
Explain what this means and why...
asked 1 hour ago