Question

In: Physics

A solid sphere (mass 0.324 kg, radius 0.245 m) sits at rest on a horizontal floor....

A solid sphere (mass 0.324 kg, radius 0.245 m) sits at rest on a horizontal floor. You begin to push the sphere until it is rotating at 42.6 Hz. Assume the sphere always moves by rolling without slipping. Find the work you have done to accelerated the sphere, in J.

Solutions

Expert Solution

Moment of Inertia along diameter and passing through its centre of mass is given by

where

M is mass of solid sphere

R is radius of solid sphere

Above is diagram of solid sphere where O is its centre of Mass and A is a point at a distance R through which an axis parallel to COM axis is passing

Now we need to find Moment of Inertia along axis passing through point A using Parallel Axis theorem which says

Given information

Mass of solid sphere = M = 0.324 Kg

Radius of solid sphere = R = 0.245 m

Frequency of rotation = v = 42.6 Hz

As mentioned in problem that solid sphere rotates without slipping, thus work done will be same as Rotational Kinetic Energy for solid sphere

work done = W= 973.37 J


Related Solutions

A 2.3 kg solid sphere (radius = 0.10 m ) is released from rest at the...
A 2.3 kg solid sphere (radius = 0.10 m ) is released from rest at the top of a ramp and allowed to roll without slipping. The ramp is 0.70 m high and 5.7 m long. A.) When the sphere reaches the bottom of the ramp, what is its total kinetic energy? B.) When the sphere reaches the bottom of the ramp, what is its rotational kinetic energy? C.) When the sphere reaches the bottom of the ramp, what is...
A box of mass 18.0 kg sits at rest on a horizontal surface. The coefficient of...
A box of mass 18.0 kg sits at rest on a horizontal surface. The coefficient of kinetic friction between the surface and the box is 0.300. The box is initially at rest, and then a constant force of magnitude FF and direction 39.0 ∘∘ below the horizontal is applied to the box; the box slides along the surface. A. What is F if the box has a speed of 6.00 m/s after traveling a distance of 8.00 mm? Express your...
A box of mass M sits on the floor of an elevator at rest. Gravity (which...
A box of mass M sits on the floor of an elevator at rest. Gravity (which has a strength set by the local acceleration due to gravity g) pulls the box and the floor pushes the box. The net or total force on the box is zero. What is the force on the box from the floor? Give both the magnitude and the direction. Now imagine that the elevator is accelerating upwards at acceleration a. Now the two forces on...
Part A) A solid sphere of mass M and radius R is mounted on an axle...
Part A) A solid sphere of mass M and radius R is mounted on an axle through its center. The axle is attached to a horizontal spring of constant k, and the sphere rolls back and forth without slipping. Derive an expression for the total energy of this system in terms of the displacement of the spring x, speed v of the center-of-mass of the sphere when its displacement is x, and M, and k. Part B) Derive the expression...
A solid sphere of mass 0.750 kg and radius 5.00 cm is spun up to an...
A solid sphere of mass 0.750 kg and radius 5.00 cm is spun up to an angular velocity 10.0 rad/s. The sphere is dropped from a low height onto a flat platform of mass 5.00 kg. The sphere begins to skid and move along the platform until it rolls without slipping. The coefficient of kinetic friction between the sphere and the platform is 0.70. The coefficient of friction between the platform and the ground is 0.05, and the platform begins...
A mass m = 17 kg is pulled along a horizontal floor, with a coefficient of...
A mass m = 17 kg is pulled along a horizontal floor, with a coefficient of kinetic friction μk = 0.06, for a distance d = 5.1 m. Then the mass is continued to be pulled up a frictionless incline that makes an angle θ = 28° with the horizontal. The entire time the massless rope used to pull the block is pulled parallel to the incline at an angle of θ = 28° (thus on the incline it is...
A mass m = 16 kg is pulled along a horizontal floor with NO friction for...
A mass m = 16 kg is pulled along a horizontal floor with NO friction for a distance d =8.4 m. Then the mass is pulled up an incline that makes an angle ? = 25
A mass m = 17 kg is pulled along a horizontal floor, with a coefficient of...
A mass m = 17 kg is pulled along a horizontal floor, with a coefficient of kinetic friction ?k = 0.06, for a distance d = 6.7 m. Then the mass is continued to be pulled up a frictionless incline that makes an angle ? = 33° with the horizontal. The entire time the massless rope used to pull the block is pulled parallel to the incline at an angle of ? = 33° (thus on the incline it is...
A mass m = 17 kg is pulled along a horizontal floor with NO friction for...
A mass m = 17 kg is pulled along a horizontal floor with NO friction for a distance d =5.7 m. Then the mass is pulled up an incline that makes an angle θ = 34° with the horizontal and has a coefficient of kinetic friction μk = 0.38. The entire time the massless rope used to pull the block is pulled parallel to the incline at an angle of θ = 34° (thus on the incline it is parallel...
A mass m = 13 kg is pulled along a horizontal floor with NO friction for...
A mass m = 13 kg is pulled along a horizontal floor with NO friction for a distance d =7.4 m. Then the mass is pulled up an incline that makes an angle θ = 32° with the horizontal and has a coefficient of kinetic friction μk = 0.31. The entire time the massless rope used to pull the block is pulled parallel to the incline at an angle of θ = 32° (thus on the incline it is parallel...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT