Question

In the figure here, a solid brass ball of mass 0.331 g will roll smoothly along a loop-the-loop track when released from rest along the straight section. The circular loop has radius R = 0.15 m, and the ball has radius r << R. (a) What is h if the ball is on the verge of leaving the track when it reaches the top of the loop? (b) If the ball is released at height h = 4R, what is the magnitude of the horizontal force component acting on the ball at point Q?

Answer #1

(a) using conservation of energy

mgh_{i} = mgh_{f} + 1/2mv^{2} + 1/2
(2/5mr^{2})w^{2}

where w = v/r

mgh_{i} = mgh_{f} + 1/2mv^{2} + 1/2
(2/5mr^{2}) (v/r)^{2}

gh_{i} = gh_{f} + v^{2} / 2 +
v^{2} / 5

gh_{i} = 2gr + 7v^{2} / 10

at the verge of leaving,

v^{2} = rg

so,

gh_{i} = 2gr + 7rg / 10

h_{i} = 2r + 7r / 10

h_{i} = 2.7r

h_{i} = 2.7 * 0.15

h_{i} = 0.405 m or 40.5 cm

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

(b) now, if h_{i} = 4r

mg(4r) = mgr + 1/2mv^{2} + 1/2 (2/5mr^{2})
(v/r)^{2}

g(4r) = gr + 1/2v^{2} + 1/2 (2/5r^{2})
(v/r)^{2}

g(4r) = gr + 7v^{2} / 10

3gr = 7v^{2} / 10

v^{2} = 30gr / 7

so,

F = mv^{2} / r

F = m*30gr / 7r

F = m*30*g / 7

F = 0.013902 N

or

F = 1.39e-2 N

In the figure here, a solid brass ball of mass 0.319 g will roll
smoothly along a loop-the-loop track when released from rest along
the straight section. The circular loop has radius R =
0.15 m, and the ball has radius r <<
R.
(a) What is h if the ball is on the verge
of leaving the track when it reaches the top of the loop?
(b) If the ball is released at height h =
6R, what is...

A solid sphere of radius r and mass m is released from a rest on
a track. At a height h above a horizontal surface. The sphere rolls
without slipping with its motion continuing around a loop of radius
R<<r
A) If R=0.3h, what is the speed of the sphere when it reaches
the top of the loop? Your response must be expressed in terms of
some or all of the quantities given above and physical and
numerical constants
B)...

A ball of mass M and radius R rolls smoothly from rest down a
ramp and onto a circular loop of radius 0.47 m. The initial height
of the ball is h = 0.35 m. At the loop bottom, the magnitude of the
normal force on the ball is 2.0 Mg. The ball consists of an outer
spherical shell (of a certain uniform density) that is glued to a
central sphere (of a different uniform density). The rotational
inertia of...

A solid brass cylinder and a solid wood cylinder have the same
radius and mass (the wood cylinder is longer). Released together
from rest, they roll down an incline. (a) Which cylinder reaches
the bottom first, or do the tie? (b) The wood cylinder is then
shortened to match the length of the brass cylinder, and the brass
cylinder is drilled out along its long (central) axis to match the
mass of the wood cylinder. Which cylinder now wins the...

A solid 0.5750-kg ball rolls without slipping down a track
toward a loop-the-loop of radius R = 0.6550 m. What minimum
translational speed vmin must the ball have when it is a height H =
1.026 m above the bottom of the loop, in order to complete the loop
without falling off the track?

A solid 0.595-kg ball rolls without slipping down a track toward
a loop-the-loop of radius R = 0.7350 m. What minimum translational
speed vmin must the ball have when it is a height H = 1.091 m above
the bottom of the loop, in order to complete the loop without
falling off the track?

A tennis ball is a hollow sphere with a thin wall. It is set
rolling without slipping at 4.10 m/s on a horizontal section of a
track as shown in the figure below. It rolls around the inside of a
vertical circular loop of radius r = 48.1 cm. As the ball nears the
bottom of the loop, the shape of the track deviates from a perfect
circle so that the ball leaves the track at a point h =...

A mass m = 86 kg slides on a frictionless track that has a drop,
followed by a loop-the-loop with radius R = 19.7 m and finally a
flat straight section at the same height as the center of the loop
(19.7 m off the ground). Since the mass would not make it around
the loop if released from the height of the top of the loop (do you
know why?) it must be released above the top of the...

Two objects of equal mass m are at rest at the top of a hill of
height h. Object 1 is a circular hoop of radius r, and object 2 is
a solid disc, also of radius r. The object are released from rest
and roll without slipping.
A) Provide expressions for the LINEAR VELOCITY of each object
once it reaches the bottom of the hill. Careful - you should
provide two answers!
B) Considering your results from part A,...

A billiard ball with a mass of m and a radius of r is rolling down without friction along an inclined plane with a slope of Θ at h height from the floor.
(1) Find an inertial moment for the center of a billiard ball. Here the mass distribution of billiard balls is assumed to be uniform.
(2) What is the speed of a billiard ball when it reaches the floor?
((1)If you can't solve the question yourself, use inertia...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 12 minutes ago

asked 15 minutes ago

asked 27 minutes ago

asked 27 minutes ago

asked 33 minutes ago

asked 41 minutes ago

asked 48 minutes ago

asked 48 minutes ago

asked 50 minutes ago

asked 53 minutes ago

asked 1 hour ago

asked 1 hour ago