Question

A small ball (mass 0.1 kg) rolls around on the inside of a
funnel (cone), in a horizontal circle of radius R = 0.1 m. The ball
experiences negligible rolling friction and is traveling at
constant speed v. If the inside surface of the funnel makes an
angle of 45° to the horizontal (or vertical), and you assume g = 10
m/s2, what is the speed v of the ball? (Hint: think of the role of
the normal force by the funnel on the ball.)

This link (
https://d2vlcm61l7u1fs.cloudfront.net/media%2F323%2F3230436e-fb79-457b-83ce-574728ac79b9%2FphpIQN8Ce.png
) provides the diagram of the situation described in the
problem.

Answer #1

A spherical bowling ball with mass m = 4.2 kg and radius R = 0.1
m is thrown down the lane with an initial speed of v = 8.1 m/s. The
coefficient of kinetic friction between the sliding ball and the
ground is μ = 0.28. Once the ball begins to roll without slipping
it moves with a constant velocity down the lane.
3)
How long does it take the bowling ball to begin rolling without
slipping?
4)
How far...

In her hand, a softball pitcher swings a ball of mass 0.254 kg
around a vertical circular path of radius 59.4 cm before releasing
it from her hand. The pitcher maintains a component of force on the
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the complete path. The speed of the ball at the top of the circle
is 15.7 m/s. If she releases the ball at the bottom of the circle,
what is its...

A 5.39-kg ball hangs from the top of a vertical pole by a
2.45-m-long string. The ball is struck, causing it to revolve
around the pole at a speed of 4.79 m/s in a horizontal circle with
the string remaining taut. Calculate the angle, between 0° and 90°,
that the string makes with the pole. Take g = 9.81 m/s2.
What is the tension of the string?

The figure shows a ball with mass m = 0.450 kg attached
to the end of a thin rod with length L = 0.415 m and
negligible mass. The other end of the rod is pivoted so that the
ball can move in a vertical circle. The rod is held horizontally as
shown and then given enough of a downward push to cause the ball to
swing down and around and just reach the vertically upward
position, with zero speed...

A light, nonstretching cable is wrapped around a solid cylinder
with mass 88 kg and radius 0.19 m. The cylinder rotates with
negligible friction about a stationary horizontal axis. We attach
the free end of the cable to a block of mass 48 kg, and release the
block from rest at a distance 3.9 m above the floor. As the block
falls, the cable unwinds without stretching or slipping. Find the
angular speed of the cylinder (in radians/s) the moment...

3-A 1.0 kg block slides down an inclined plane of 39
0 from the horizontal. If the
block starts from rest and hits the bottom in 5.1 s,
what is the speed of the block, in the unit m/s, at the bottom of
the incline? Assume a frictionless plane.
4-A bus negotiates a turn of radius 103 m while traveling at a
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1. For a stationary ball of mass m = 0.200 kg hanging from a
massless string, draw arrows (click on the “Shapes” tab) showing
the forces acting on the ball (lengths can be arbitrary, but get
the relative lengths of each force roughly correct). For this case
of zero acceleration, use Newton’s 2nd law to find the
magnitude of the tension force in the string, in units of Newtons.
Since we will be considering motion in the horizontal xy plane,...

12. Through what angle in degrees does a 31 rpm record turn in
0.27 s
13. Starting from rest, the same torque is applied to a solid
sphere and a hollow sphere. Both spheres have the same size and
mass, and both are rotating about their centers. After some time
has elapsed, which sphere will be rotating faster?
answer choices:
a. hollow sphere
b. They will be rotating equally fast
c. solid sphere
14. In movies, it often happens that...

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