Question

In: Physics

a 1m radius cylinder with a mass of 852.9 kg rolls without slipping down a hill...

a 1m radius cylinder with a mass of 852.9 kg rolls without slipping down a hill which is 82.1 meters high. at the bottom of the hill what friction of its total kinetic energy is invested in rotational kinetic energy

Expert Solution

Gravitational acceleration = g = 9.81 m/s²

Mass of the cylinder = M = 852.9 kg

Radius of the cylinder = R = 1 m

Moment of inertia of the cylinder = I

Height of the hill = H = 82.1 m

Velocity of the cylinder at the bottom of the hill = V

Angular speed of the cylinder at the bottom of the hill = = V/R

Rotational kinetic energy of the cylinder at the bottom of the hill = KE_R

Translational kinetic energy of the cylinder at the bottom of the hill = KE_T

Total kinetic energy of the cylinder at the bottom of the hill = KE

Ratio of the rotational kinetic energy and the total kinetic energy = f

f = 1/3

Fraction of the total kinetic energy of the cylinder invested in rotational kinetic energy at the bottom of the hill = 1/3

genius_generous answered 2 years ago

A thin-walled hollow cylinder with mass m1 and radius R1 rolls without slipping on the inner...

A thin-walled hollow cylinder with mass m1 and radius R1 rolls without slipping on the inner wall of a larger thin-walled hollow cylinder with mass m2 and radius R2 >> R1. Both cylinders' axes are aligned and horizontal, and some magical mechanism ensures this perfect friction contact between them. Unfortunately for you, the larger cylinder rolls without slipping on a horizontal surface. Describe the motion including small oscillation frequencies near any equilibria if the systems is released from rest with...

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...

3) A solid cylinder with mass 4kg and radius r=0.5 m rolls without slipping from a...

3) A solid cylinder with mass 4kg and radius r=0.5 m rolls without slipping from a height of 10 meters on an inclined plane with length 20 meters. a) Find the friction force so that it rolls without slippingb) Calculate the minimum coefficient of rolling friction muc) Calculate its speed as it arrives at the bottom of the inclined plane.

a spherical shell of mass 2.0 kg rolls without slipping down a 38 degree slope A)...

a spherical shell of mass 2.0 kg rolls without slipping down a 38 degree slope A) Find the acceleration, the friction force, and the minimum coefficient of friction needed to prevent slipping. B) if the spherical starts from rest at the top how fast is the center of mass moving at the bottom of the slope if the slope is 1.50 m high? PLEASE INCLUDE DIAGRAM

A hollow, spherical shell with mass 1.80 kg rolls without slipping down a slope angled at...

A hollow, spherical shell with mass 1.80 kg rolls without slipping down a slope angled at 40.0 ∘. Part A Find the acceleration. Take the free fall acceleration to be g = 9.80 m/s2 partB Find the friction force. Take the free fall acceleration to be g = 9.80 m/s2 Part C Find the minimum coefficient of friction needed to prevent slipping.

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?

Problem: a unifiorm hoop of mass m and radius r rolls without slipping on a fixed...

Problem: a unifiorm hoop of mass m and radius r rolls without slipping on a fixed cylinder of radius R. if the hoop is stats rolling from rest on top of the bigger cylinder, use the method of Lagrange multipliers to find the point at which the hoop fall off the cylinder. Question: I know how to derive Lagrange equeation. but to use the method of Lagrange multipliers, i have to finde constrain. solution says that f1, f2 are constrain....

A hollow ball, made of a thin plastic shell, rolls down a rough hill (no slipping)...

A hollow ball, made of a thin plastic shell, rolls down a rough hill (no slipping) of height h? from rest and across a level ground. It then approaches another hill, but this one is smooth and frictionless. a) Draw a diagram of this situation. (4 points) b) Write down the energy equation which represents the first half of the journey and simplify it to find an expression for the maximum linear velocity of the ball. (4 points) c) Write...

A ball rolls down along an incline without slipping. A block slides down from the same...

A ball rolls down along an incline without slipping. A block slides down from the same incline without friction. Assuming the two objects start from the same position, which of the following statement is correct?

A solid cylinder of radius 10 cm and mass 12 kg starts from rest and rolls...

A solid cylinder of radius 10 cm and mass 12 kg starts from rest and rolls without slipping a distance L = 6.0 m down a roof that is inclined at angle  = 30o . a. What is the linear speed and the angular speed of the cylinder about its center as it leaves the roof? b. The roof’s edge is at height H = 5.0 m. How far horizontally from the roof’s edge does the cylinder hit the...