Question

In: Physics

A uniform solid cylindrical log begins rolling without slipping down a ramp that rises 15.0 ∘...

A uniform solid cylindrical log begins rolling without slipping down a ramp that rises 15.0 ∘ above the horizontal. After it has rolled 4.50 m along the ramp, what is the magnitude of the linear acceleration of its center of mass?

Solutions

Expert Solution

First, find the vertical distance covered

Consider the incline

=================

When the log rolls, initial potential energy is converted to rotational kinetic energy and translational kintic energy

-----------

Moment of inertia of solid cylinder,

and angular velocity,

------------

=========

Given that the log starts from rest

Use formula to find acceleration

ANSWER :

======================

genius_generous answered 4 months ago

Next > < Previous

Related Solutions

1. A solid uniform cylinder is rolling without slipping. What fraction of this cylinder's kinetic energy...

1. A solid uniform cylinder is rolling without slipping. What fraction of this cylinder's kinetic energy is rotational? (Note: the moment of inertia of a cylinder of mass M and radius R rotating about its central axis is 0.5MR2.) A 1/3 B 2/3 C 1/2 D 1/4 E 3/4 2. A public art installation consists of three 25-kg glass sculptures hung side-by-side with steel wires of length 1.00 m, 2.00 m and 3.00 m. If the wires all have the...

Consider a cylinder rolling, without slipping, on an inclined flat surface (a ramp) that forms an...

Consider a cylinder rolling, without slipping, on an inclined flat surface (a ramp) that forms an angle  = 30 º with respect to the horizontal direction. An external force F = 10 N parallel to the ramp is pushing the cylinder in the uphill direction, without creating any torque (that is, the force is acting directly on the center of mass of the cylinder). If the cylinder is released at a time t = 0 with a linear velocity...

A disc and solid sphere are both rolling without slipping so that both have a kinetic...

A disc and solid sphere are both rolling without slipping so that both have a kinetic energy of 294. What is the translational kinetic energy of the disc ? What is the translational kinetic energy of the solid sphere ?

A, A thin cylindrical shell is released from rest and rolls without slipping down an inclined...

A, A thin cylindrical shell is released from rest and rolls without slipping down an inclined ramp, a distance s, that makes an angle of θ with the horizontal. If the coefficient of friction is µK, what is the speed at the bottom of the ramp? 2, A force P pushes a block at an angle 30° from the vertical across the ceiling. There is a coefficient of kinetic friction, µk. What is the acceleration?

A uniform hoop of mass M and radius R rolls down an incline without slipping, starting...

A uniform hoop of mass M and radius R rolls down an incline without slipping, starting from rest. The angle of inclination of the incline is θ. a. After moving a distance L along the incline, what is the angular speed ω of the hoop? b. If the coefficient of static friction between the hoop and the incline is µs = 1/3, what is the greatest possible value of θ such that no slipping occurs between the hoop and the...

A bowling ball rolls without slipping up a ramp. If the speed at the bottom of...

A bowling ball rolls without slipping up a ramp. If the speed at the bottom of the ramp is 2.85 m/s and the height of the ramp is 0.525 m, what is the speed of the ball at the top of the ramp?

A uniform solid ball of m=4.0 kg and radius r rolls smoothly down a ramp. The...

A uniform solid ball of m=4.0 kg and radius r rolls smoothly down a ramp. The ball starts from rest. The ball descends a vertical height of 6.0 m to reach the bottom of the ramp. What is its speed at the bottom?

A solid, uniform disk of radius 0.250 m and mass 53.2 kg rolls down a ramp...

A solid, uniform disk of radius 0.250 m and mass 53.2 kg rolls down a ramp of length 4.70 m that makes an angle of 12.0° with the horizontal. The disk starts from rest from the top of the ramp. (a) Find the speed of the disk's center of mass when it reaches the bottom of the ramp. m/s (b) Find the angular speed of the disk at the bottom of the ramp. rad/s

A 2.2 kg hoop 1.2 in diameter is rolling to the right without slipping on a...

A 2.2 kg hoop 1.2 in diameter is rolling to the right without slipping on a horizontal floor at a steady 2.6 rad/s. A uniform cylinder with its outer radius two times it’s inner radius with the same mass, same diameter as the hoop and also rolls without slipping with the same angular frequency. What is the ratio of rotational kinetic energies between the hoop and the uniform cylinder? What is the ratio of the rotational frequency between the hoop...

A solid 0.5350-kg ball rolls without slipping down a track toward a loop-the-loop of radius R...

A solid 0.5350-kg ball rolls without slipping down a track toward a loop-the-loop of radius R = 0.8150 m. What minimum translational speed vmin must the ball have when it is a height H = 1.276 m above the bottom of the loop, in order to complete the loop without falling off the track?

Subjects