Question

A ball of mass m is
tied to a string and is rotating in a vertical plane. The string is
elastic (it stretches), which causes the path to be elongated
vertically rather than perfectly circular. At the top of the path,
the speed has the minimum value that still allows the ball to
complete its circular path.

Find: the length of the string when it makes an angle θ with respect to the horizontal.

The following quantities are known:

Mass of the ball , m

Elastic constant of the string, k

Length of the string when the ball is at the top , r0

angle θ

To solve the problem

a)
Start by
writing the conservation of energy; you know something about the
top position, consider that to be your initial; the final state is
when the string is at the angle θ. Taking
the zero level for potential energy at the center of the circle
would make the equation simpler.

b)
Once you wrote
the equation of conservation of energy, try to express each term as
a function of r and known
quantities. For example:

- x in the elastic potential energy formula is r-r0;

- The velocity at the top is at a minimum, so you can express it as a function of r0;

For the velocity at the final position, draw a free body diagram, look at the net force along the string and apply Newton’s Second Law along the string. The acceleration is, of course, the centripetal acceleration ;

-h at the final position can be expressed using the angle and r.

Answer #1

If you have any doubt, feel free to ask.

Alright Dude, If that worked for you... dont forget to give THUMBS UP.(that will work for me!)

Thank you!

A tennis ball connected to a string is spun around in a
vertical, circular path at a uniform speed. The ball has a mass m =
0.154 kg and moves at v = 5.16 m/s. The circular path has a radius
of R = 1.01 m
1) What is the magnitude of the tension in the string when the
ball is at the bottom of the circle?
2) What is the magnitude of the tension in the string when the...

A tennis ball connected to a string is spun around in a
vertical, circular path at a uniform speed. The ball has a mass m =
0.15 kg and moves at v = 4.89 m/s. The circular path has a radius
of R = 0.94 m
What is the minimum velocity so the string will not go slack as
the ball moves around the circle?

A small ball of clay of mass m hangs from a string of length L
(the other end of which is fixed). A seond ball of clay of mass m/3
is to be launched horizontally out of a spring with spring constant
k. Once launched, the second ball will collide with and stick to
the hanging ball, and they'll follow a circular path around the
fixed end of the string.
A) Determine an expression for the distance (change in x)...

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,...

A simple pendulum consists of a ball of mass m suspended from
the ceiling using a string of length L. The ball is displaced from
its equilibrium position by a small angle θ and released. Which one
of the following statements concerning this situation is
correct?
(a) If the mass were increased, the period of the pendulum would
increase.
(b) The frequency of the pendulum does not depend on the
acceleration due to gravity.
(c) If the length of the...

A wooden plank of length L and mass M is hanging vertically
attached to the ceiling by a frictionless hinge. The plank is in
equilibrium, when struck by a bullet of mass m that has velocity
given by the equation below. The bullet hits the plank at a
distance D (D< L) from the ceiling and remains stuck in the
plank.
~v = vxˆi + vyˆj -> velocity of the bullet.
a) What is the angular acceleration of the plank...

A ball with a mass of 270 g is tied to a light string that has a
length of 2.40 m. The end of the string is tied to a hook, and the
ball hangs motionless below the hook. Keeping the string taut, you
move the ball back and up until it is a vertical distance of 1.16 m
above its equilibrium point. You then release the ball from rest,
and it oscillates back and forth, pendulum style. As usual,...

A rock is tied to a string and spun in a circle of radius 1.4 m
as shown in the figure below. The speed of the rock is 13 m/s.
(c) What is the total force on the rock directed toward the
center of its circular path? Express your answer in terms of the
(unknown) tension T in the string. (Use the following as necessary:
?.) F = (d) Apply Newton's second law along both the vertical and
the horizontal...

A block of mass m is moving in a circular path on a tabletop.
The radius of the circle is r and the object's speed is v. What is
the initial angular momentum of the system? What is the initial
kinetic energy of the system?
Suppose the mass was being pulled in circular motion by a
string. The string is threaded through a small hole on the top of
the table, and a person pulls on the string until it...

In a spring gun system, a spring with a spring force constant
350 N/mN/m , is compressed 0.11 mm . When fired, 81.0 %%
of the elastic potential energy stored in the spring is eventually
converted into kinetic energy of a 6.40×10−2 kgkg
uniform ball that is rolling without slipping at the base of a
ramp. The ball continues to roll without slipping up the ramp with
90.0 %% of the kinetic energy at the bottom converted into an
increase in...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 1 minute ago

asked 7 minutes ago

asked 8 minutes ago

asked 13 minutes ago

asked 34 minutes ago

asked 48 minutes ago

asked 58 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago