A merry-go-round modeled as a disk of mass M = 9.00 101 kg and radius R =...

A merry-go-round modeled as a disk of mass M = 9.00 10¹ kg and radius R = 2.20 m is rotating in a horizontal plane about a frictionless vertical axle (see figure).

(a) After a student with mass m = 88.0 kg jumps onto the merry-go-round, the system's angular speed decreases to 2.10 rad/s. If the student walks slowly from the edge toward the center, find the angular speed of the system when she reaches a point 0.490 m from the center.
rad/s

(b) Find the change in the system's rotational kinetic energy caused by her movement to the center.
J

(c) Find the work done on the student as she walks to r = 0.490 m.
J

Use the values from the PRACTICE IT section to answer this exercise.

(a) Find the angular speed of the merry-go-round before the student jumped on, assuming the student didn't transfer any momentum or energy as she jumped on the merry-go-round.
rad/s

(b) By how much did the kinetic energy of the system change when the student jumped on? Notice that energy is lost in this process, as should be expected, since it is essentially a perfectly inelastic collision.
KE_f − KE_i = J

Solutions

Expert Solution

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

A disk-shaped merry-go-round of radius 2.63 m and mass 155 kg rotates freely with an angular...

A disk-shaped merry-go-round of radius 2.63 m and mass 155 kg rotates freely with an angular speed of 0.570 rev/s. A 59.4-kg person running tangential to the rim of the merry-go-round at 3.82 m/s jumps onto its rim and holds on. Before jumping on the merry-go-round, the person was moving in the same direction as the merry-go-round's rim. (a) Does the kinetic energy of the system increase, decrease, or stay the same when the person jumps on the merry-go-round? (b)...

A 2.20-m radius playground merry-go-round has a mass of 101.5 kg and is rotating with an...

A 2.20-m radius playground merry-go-round has a mass of 101.5 kg and is rotating with an angular velocity of 0.91 rev/s. What is its angular velocity after a 38.4-kg child gets onto it by grabbing its outer edge? The child is initially at rest. Express your answer in revs/s.

Bubba (m=100kg) and Sally (m=60kg) are playing on a merry-go-round. Treat the merry-go-round as a disk...

Bubba (m=100kg) and Sally (m=60kg) are playing on a merry-go-round. Treat the merry-go-round as a disk with mass 100 kg and radius 1.3 m. Both Bubba and Salley are at the edge of the disk when the disk is rotating at .25 revolutions per second. Suppse Bubba moves inward so that he is now exactly at the center. Treat the two children as point masses. Assuming there is no external torques or forces, A) What is the new rotational speed...

Consider the child's playground merry-go-round wheel. Merry Go Round If the steel disk has mass of...

Consider the child's playground merry-go-round wheel. Merry Go Round If the steel disk has mass of 200 kg and a radius of 2 meters you can make it spin by applying a force to the rim. This torque increases the angular momentum of the disk. Suppose the force is 20 newtons. How long would you have to apply it to get the wheel spinning 5 times a minute? What would happen to the rate of spin if you then jumped...

A merry-go-round with a a radius of R = 1.98 m and moment of inertia I...

A merry-go-round with a a radius of R = 1.98 m and moment of inertia I = 193 kg-m2 is spinning with an initial angular speed of ω = 1.45 rad/s in the counter clockwise direection when viewed from above. A person with mass m = 67 kg and velocity v = 4.9 m/s runs on a path tangent to the merry-go-round. Once at the merry-go-round the person jumps on and holds on to the rim of the merry-go-round. 1)...

A merry-go-round consists of a uniform ring of mass 2M and radius R attached to a...

A merry-go-round consists of a uniform ring of mass 2M and radius R attached to a central post with four light, uniform rods, each of mass M/4 and length R. Identical twins sit opposite one another where two of the rods join the ring. The mass of each child is M. At time t = 0, the system is rotating with angular speed ω0. The twins then simultaneously pull themselves toward one another along their respective rods, until each twin...

A merry go round (a disk I=(1/2) MR2, M=200 kg, R=2.0 m) rotates initially at 0.3...

A merry go round (a disk I=(1/2) MR2, M=200 kg, R=2.0 m) rotates initially at 0.3 rad/s. A child of mass 40 kg is dropped onto the merry go round at a distance of 1.5 m from the axis of rotation. How fast is the child moving after it comes to turn with the merry go round?

A disk with mass m = 11.8 kg and radius R = 0.31 m begins at...

A disk with mass m = 11.8 kg and radius R = 0.31 m begins at rest and accelerates uniformly for t = 17.2 s, to a final angular speed of ω = 31 rad/s. 1.What is the angular acceleration of the disk? 2. What is the angular displacement over the 17.2 s? 3. What is the moment of inertia of the disk? 4. What is the change in rotational energy of the disk?

A 50.0 kg child stands at the rim of a merry-go-round of radius 1.50 m, rotating...

A 50.0 kg child stands at the rim of a merry-go-round of radius 1.50 m, rotating with an angular speed of 2.50 rad/s. (a) What is the child's centripetal acceleration? m/s2 (b) What is the minimum force between her feet and the floor of the merry-go-round that is required to keep her in the circular path? N (c) What minimum coefficient of static friction is required? Is the answer you found reasonable? In other words, is she likely to be...

A horizontal 808-N merry-go-round is a solid disk of radius 1.54 m, started from rest by...

A horizontal 808-N merry-go-round is a solid disk of radius 1.54 m, started from rest by a constant horizontal force of 50.9 N applied tangentially to the edge of the disk. Find the kinetic energy of the disk after 3.08 s.

Subjects