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A particle of mass m slides down a fixed, frictionless sphere of radius R. starting from...
5. A particle of mass m slides without friction and starting from rest down a block...
5. A particle of mass m slides without friction and starting from rest down a block of mass M in which the surface is shaped into a quadrant of a circle of radius R. The block also slides without friction on a table top. Choose two suitable generalized coordinates a) Using the Lagrange-multiplier formalism, find the equations of motion of the mass and the block and the reaction force of the block on the mass (ie. the constraint force b)...
Problem 3 10 marks A particle of mass m slides down a frictionless incline of angle...
Problem 3 10 marks A particle of mass m slides down a frictionless incline of angle a, mass M and length L which is on a horizontal frictionless plane (see the Figure). If the particle starts initially from rest at the top of the incline, prove that the time for the particle to reach the bottom is given by, 2L(M + m sina) (M + m)g sina To setup the problem, choose a fixed vertical xy coordinate system as in...
2. A small box of mass m is kept on a fixed, smooth sphere of radius...
2. A small box of mass m is kept on a fixed, smooth sphere of radius R at a position where the radius through the box makes an angle of 30° with the vertical. The box is released from the position. (a) What is the force exerted by the sphere on the box just after the release? (b) Find the distance travelled by the box before it leaves contact with the sphere. 3. A particle is suspended from a fixed...
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...
5. A small mass m starts from rest and slides from the top of a fixed...
5. A small mass m starts from rest and slides from the top of a fixed sphere of radius r. (a) If the sphere is frictionless, at what angle θ from the vertical does the mass leave the surface? (b) Suppose there is friction between the mass and the sphere with friction coefficient =0.1. What is the minimum angle θmin at which the mass will start to slide along the sphere? (c) The mass is now placed just past this...
A block of mass m slides down a frictionless ramp to a loop of radius R,...
A block of mass m slides down a frictionless ramp to a
loop of radius R, also frictionless. It's initial height
above the bottom of the loop is ?h = 3R and the
block starts at rest.
What is the magnitude of the normal force that the track of the
loop exerts on the block at position 2? You can assume that the
block is exactly at the horizontal height of the center of the loop
when it reaches position...
A particle of mass m starts at rest on top of a smooth fixed hemisphere of...
A particle of mass m starts at rest on top of a smooth fixed hemisphere of radius R. Find the force of constant, and determine the angle at which the particle leaves the hemisphere.
A smooth sphere of radius R rests on a horizontal plane. A small mass is placed...
A smooth sphere of radius R rests on a horizontal plane. A small mass is placed on top of the sphere and slides without friction down it. Find a) the angle and speed at which the small mass leaves the surface of the sphere and b) the angle and speed with which the mass strikes the ground.
. A small mass m starts from rest and slides from the top of a fixed...
. A small mass m starts from rest and slides from the top of a fixed sphere of radius r (b) Suppose there is friction between the mass and the sphere with friction coefficient μ,-0.1. what is the minimum angle Emin at which the mass will start to slide along the sphere? (c) The mass is now placed just past this minimum angle and released. The coefficient of kinetic friction k is small but not zero. Does the mass fly...
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...
5. A particle of mass m slides without friction and starting from rest down a block of mass M in which the surface is shaped into a quadrant of a circle of radius R. The block also slides without friction on a table top. Choose two suitable generalized coordinates a) Using the Lagrange-multiplier formalism, find the equations of motion of the mass and the block and the reaction force of the block on the mass (ie. the constraint force b)...
Problem 3 10 marks A particle of mass m slides down a frictionless incline of angle a, mass M and length L which is on a horizontal frictionless plane (see the Figure). If the particle starts initially from rest at the top of the incline, prove that the time for the particle to reach the bottom is given by, 2L(M + m sina) (M + m)g sina To setup the problem, choose a fixed vertical xy coordinate system as in...
2. A small box of mass m is kept on a fixed, smooth sphere of radius R at a position where the radius through the box makes an angle of 30° with the vertical. The box is released from the position. (a) What is the force exerted by the sphere on the box just after the release? (b) Find the distance travelled by the box before it leaves contact with the sphere. 3. A particle is suspended from a fixed...
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...
5. A small mass m starts from rest and slides from the top of a fixed sphere of radius r. (a) If the sphere is frictionless, at what angle θ from the vertical does the mass leave the surface? (b) Suppose there is friction between the mass and the sphere with friction coefficient =0.1. What is the minimum angle θmin at which the mass will start to slide along the sphere? (c) The mass is now placed just past this...
A block of mass m slides down a frictionless ramp to a
loop of radius R, also frictionless. It's initial height
above the bottom of the loop is ?h = 3R and the
block starts at rest.
What is the magnitude of the normal force that the track of the
loop exerts on the block at position 2? You can assume that the
block is exactly at the horizontal height of the center of the loop
when it reaches position...
A particle of mass m starts at rest on top of a smooth fixed hemisphere of radius R. Find the force of constant, and determine the angle at which the particle leaves the hemisphere.
. A small mass m starts from rest and slides from the top of a fixed sphere of radius r (b) Suppose there is friction between the mass and the sphere with friction coefficient μ,-0.1. what is the minimum angle Emin at which the mass will start to slide along the sphere? (c) The mass is now placed just past this minimum angle and released. The coefficient of kinetic friction k is small but not zero. Does the mass fly...
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...
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