Consider a solid sphere of mass m and radius r being released from a height h...
Consider a solid sphere of mass m and radius r being released from a height h (i.e., its center of mass is initially a height h above the ground). It rolls without slipping and passes through a vertical loop of radius R.
a. Use energy conservation to determine the tangential and angular velocities of the sphere when it reaches the top of the loop.
b. Draw a force diagram for the sphere at the top of the loop and write down Newton´s second law in the radial direction.
c. What is the minimum height from which the sphere must be released so that it doesn’t fall off the track at the top of the loop?
d. Neglecting its moment of inertia, would the minimum height be more or less than the one you calculated? Explain.
Homework Answers
a) mgh=mg2R+0.5mv^2+0.5 (Moment Of Inertia) Angular Velocity^2
mgh=2Rmg+0.5mv^2+0.5(2/5mr^2) (v/r)^2
mgh=2Rmg+0.5mv^2+0.2mv^2
mgh=2Rmg+0.7mv^2
gh-2Rg/0.7=v^2
v= root(gh-2Rg)
Angular velocity=v/r
b) On the top most pont Normal reaction and weight both will be point down. So N+mg=mv^2/R
c) To complete the circle minimum speed required is root(5gr) at the bottom so mgh=0.5m5gr (considering centre of mass only)
h=2.5g
d) If we neglect the MOI that rotaion the minimum heoght will be greater as we need to give more energy so must fall from greater height
Add Answer to:
Consider a solid sphere of mass m and radius r being released
from a height h...
AP Physics C FRQ 3. A sphere of mass m and radius r is released from...
AP Physics C FRQ
3. A sphere of mass m and radius r is released from rest at the top of a curved track of height H. The sphere travels down the curved track and around a loop of radius R. The sphere rolls without slipping during the entire motion. Point A on the loop is at height R, and point B is at the top of the loop. The rotational inertia of the sphere is 2mr2/s. Express all of...
A small solid glass sphere, with a mass m and radius r, is placed on the...
A small solid glass sphere, with a mass m and radius r, is placed on the inclined section of the metal track shown below, such that its lowest loop. The sphere is then released from rest, and it rolls on the track without slipping. In your analysis, use the approximation that the radius radius R of the loop and the height h. (Use the following as necessary: M, R, and g for the acceleration of gravity.) Solid sphere of mass...
A small solid porcelain sphere, with a mass m and radius r, is placed on the...
A small solid porcelain sphere, with a mass m and radius r, is placed on the inclined section of the metal track shown below, such that its lowest point is at a height h above the bottom of the loop. The sphere is then released from rest, and it rolls on the track without slipping. In your analysis, use the approximation that the radius r of the sphere is much smaller than both the radius R of the loop and...
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...
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 uniform solid sphere of radius r=8.60 cm starts from rest at a height h and...
A uniform solid sphere of radius r=8.60 cm starts from rest at a
height h and rolls without slipping along the loop-the-loop track
of radius R=42.00 cm as shown in Figure 9-56. What is the smallest
value of h for which the sphere will not leave the track
at the top of the loop? (h is measured from the center of
the ball at the top of the ramp to the center of the ball at the
bottom of the...
(11 points) A uniform solid sphere of mass m and radius r is placed inside a...
(11 points) A uniform solid sphere of mass m and radius r is placed inside a hemispherical bowl of radius R. The sphere is released from rest at an angle theta and rolls without slipping. (a) (6 points) Using Conservation of Energy, to find an expression for the angular speed of the sphere when it reaches the lowest point of the bowl. (b) (6 points) Find the magnitude of the centripetal acceleration of the center of mass of the sphere...
A cylinder of radius R=15.0cm and mass m=900g is released from rest at the top of...
A cylinder of radius R=15.0cm and mass m=900g is released from rest at the top of an incline of height h=10.0m. It rolls, without slipping, to the bottom of the incline. Calculate cylinder's: a)moment of inertia about its center of rotation. b)angular velocity at the bottom of the incline.
thank you Problem 5 A solid sphere of mass M-2.00 ks (uniformly distributed) and radius R...
thank you
Problem 5 A solid sphere of mass M-2.00 ks (uniformly distributed) and radius R -0.100 m starts from rest at the top of an inclined plane of length L - 1.50 m and height H-0.500 m. The coefficient of static friction between the sphere and the inclined plane is H, -0.400. The sphere rolls without slipping down the inclined plane. The moment of inertia of the sphere about an axis through its center of mass is given by...
Example2 25k A solid sphere (mass M, radius R) is released from rest at the top...
Example2 25k A solid sphere (mass M, radius R) is released from rest at the top of an inclined plane (angle ?). There is sufficient friction between the incline and the sphere to allow it to roll without slipping. (a) Draw and FBD for the sphere. (b) Find the linear acceleration of the sphere (c) Find the magnitude of the frictional force acting on the sphere. (d) Find the minimum required coefficient of friction to keep the sphere from slipping....
AP Physics C FRQ
3. A sphere of mass m and radius r is released from rest at the top of a curved track of height H. The sphere travels down the curved track and around a loop of radius R. The sphere rolls without slipping during the entire motion. Point A on the loop is at height R, and point B is at the top of the loop. The rotational inertia of the sphere is 2mr2/s. Express all of...
A small solid glass sphere, with a mass m and radius r, is placed on the inclined section of the metal track shown below, such that its lowest loop. The sphere is then released from rest, and it rolls on the track without slipping. In your analysis, use the approximation that the radius radius R of the loop and the height h. (Use the following as necessary: M, R, and g for the acceleration of gravity.) Solid sphere of mass...
A small solid porcelain sphere, with a mass m and radius r, is placed on the inclined section of the metal track shown below, such that its lowest point is at a height h above the bottom of the loop. The sphere is then released from rest, and it rolls on the track without slipping. In your analysis, use the approximation that the radius r of the sphere is much smaller than both the radius R of the loop and...
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...
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 uniform solid sphere of radius r=8.60 cm starts from rest at a
height h and rolls without slipping along the loop-the-loop track
of radius R=42.00 cm as shown in Figure 9-56. What is the smallest
value of h for which the sphere will not leave the track
at the top of the loop? (h is measured from the center of
the ball at the top of the ramp to the center of the ball at the
bottom of the...
(11 points) A uniform solid sphere of mass m and radius r is placed inside a hemispherical bowl of radius R. The sphere is released from rest at an angle theta and rolls without slipping. (a) (6 points) Using Conservation of Energy, to find an expression for the angular speed of the sphere when it reaches the lowest point of the bowl. (b) (6 points) Find the magnitude of the centripetal acceleration of the center of mass of the sphere...
thank you
Problem 5 A solid sphere of mass M-2.00 ks (uniformly distributed) and radius R -0.100 m starts from rest at the top of an inclined plane of length L - 1.50 m and height H-0.500 m. The coefficient of static friction between the sphere and the inclined plane is H, -0.400. The sphere rolls without slipping down the inclined plane. The moment of inertia of the sphere about an axis through its center of mass is given by...
Example2 25k A solid sphere (mass M, radius R) is released from rest at the top of an inclined plane (angle ?). There is sufficient friction between the incline and the sphere to allow it to roll without slipping. (a) Draw and FBD for the sphere. (b) Find the linear acceleration of the sphere (c) Find the magnitude of the frictional force acting on the sphere. (d) Find the minimum required coefficient of friction to keep the sphere from slipping....
Most questions answered within 3 hours.
-
Little’s Law: Val d’Costa is a world famous ski village in the
French Alps. Because of...
asked 1 minute ago -
Find the absolute error D for the calculation if A + B/C=D A=
9.4 +/- 0.4...
asked 14 minutes ago -
New Air Heating and Cooling, manufactures furnaces and central
air units. The company pride itself on...
asked 28 minutes ago -
A coach uses a new technique to train gymnasts. Seven
gymnasts were randomly selected and their...
asked 2 hours ago -
While rotating the tires on your car you notice a rock [mass =
0.1 Kg] stuck...
asked 4 hours ago -
Using MARS simulator, write MIPS programs according to
the following scenarios: Receive a positive integer number...
asked 6 hours ago -
An object in front of a concave mirror has a real image that is
11.5 cm...
asked 6 hours ago -
Consider the reaction, C3 H8 + O2 --> CO2 + H2O. How many
moles of O2...
asked 8 hours ago -
You and your opponent both roll a fair die. If you both roll the
same number,...
asked 8 hours ago -
In a study of the accuracy of fast food drive-through orders,
Restaurant A had 257 accurate...
asked 8 hours ago -
Identify and describe in detail the four categories of
institutions that could be included in a...
asked 8 hours 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 8 hours ago