A solid cylinder initially rolling with a translational speed of 4.5m/s rolls down a vertical drop...

A solid cylinder initially rolling with a translational speed of 4.5m/s rolls down a vertical drop of 0.625m. The cylinder has a mas of 7.25 Kg and a diameter of 0.115m. Ignore frictional losses and assume the mass of the cylinder is distributed uniformly. find transnational speed at the bottom of the drop

Expert Solution

The initial total energy at the height h is

And for a solid cylinder, the moment of inertia is

And for rolling without sliping, we have

And so, we have



The total final energy at the bottom ( similar to the preivious result with h = 0 in this case ) is

And the conservation of energy implies



So, given h = 0.625 m, and g = 9.8 m/s^2 and
And so, the translational speed at the bottom is

genius_generous answered 1 year ago

A very small ball is rolling down a vertical triangle. It rolls down 1,5m within the...

A very small ball is rolling down a vertical triangle. It rolls down 1,5m within the first second, how long will it roll on the 2nd second? We don't know if there's friction. Any ideas and tips? I'm new to this subject, so please answer thoroughly explaining each step of the solution.

A cylinder rolls up a hill, turns around, and starts rolling back down the hill. State...

A cylinder rolls up a hill, turns around, and starts rolling back down the hill. State the signs (+/-/0) of the angular acceleration and angular velocity at 3 points - one on the way up, one at the peak, and one on the way down. Briefly state your reasoning.

A hollow cylinder (hoop) is rolling on a horizontal surface at speed v = 3.3 m/s...

A hollow cylinder (hoop) is rolling on a horizontal surface at speed v = 3.3 m/s when it reaches a 16 ? incline. How far up the incline will it go? How long will it be on the incline before it arrives back at the bottom?

In a pool game, the cue ball, which has an initial speed of 4.5m/s, makes...

In a pool game, the cue ball, which has an initial speed of 4.5 m/s, makes an elastic collision with the 8-ball, which is initially at rest. After the collision, the 8-ball moves at an angle θ = 39.7° with respect to the original direction of the cue ball, as shown in the figure. At what angle φ does the cue ball travel after the collision? Assume the pool table is frictionless and the masses of the cue ball and...

In an online viral video, a truck rolls down an incline and off a vertical cliff,...

In an online viral video, a truck rolls down an incline and off a vertical cliff, falling into a valley below. The truck starts from rest and rolls down the incline, which makes an angle of 21.0° below the horizontal, with a constant acceleration of 3.37 m/s2. After rolling down the incline a distance of 30.0 m, it reaches the edge of the cliff, which is 35.0 m above ground level. How much time (in s) does it take the...

A uniform cylinder of mass m and radius r is rolling down a slope of inclination...

A uniform cylinder of mass m and radius r is rolling down a slope of inclination 30°. The cylinder rolls without slipping. At what rate does the cylinder accelerate down the slope?

A cylinder radius R is rolling down a slope, angle ø. There is sufficient friction that...

A cylinder radius R is rolling down a slope, angle ø. There is sufficient friction that the cylinder rolls without slipping, but do not assume the friction is maximum static friction. Known quantities are R, g, ø What is the linear acceleration of the cylinder down the slope?

Rotational Inertia –Rolling Kinetic Energy. A solid sphere, a hollow sphere, a hollow cylinder, and a...

Rotational Inertia –Rolling Kinetic Energy. A solid sphere, a hollow sphere, a hollow cylinder, and a solid cylinder, all of with same mass (M=0.25 kg ) and radius(R= 0.20 m) – are placed at the top of an incline at height (h= 1.5 m ). All the objects are released from rest at the same moment to roll down without slipping. Hint: search for the rotational inertia formula for each of the rolling object first. Then calculate each of them...

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

A) A solid disk rolls down an incline plane. The disk has a mass of 88...

A) A solid disk rolls down an incline plane. The disk has a mass of 88 grams, a radius of 0.15 meters, and starts at a height of 4 meters above the bottom of the ramp. What is the magnitude of the velocity of the disk at the bottom of the ramp, in m/s? B) A spring-loaded launcher has a spring constant of 230 N/m. The spring is compressed 4.5 cm. A 25 gram ball is launched exactly horizontally from...

Question