Question

A ball is tied to the top of a pole by a string. The ball rotates at 5.0m/s around the pole in a horizontal circle of radius 1.0m. What is the angle between the string and pole?

Answer #1

If you draw a free body diagram, two forces act on the ball.
Gravity vertically down and the tension in the rope directed along
the rope. The vertical component of the tension must equal the
weight of the ball (mg), and the horizontal component must deliver
the centripetal force m v^2 /R, where v is the speed of the
circular motion and R the radius of the circle. The ratio of these
forces equals the tangent of the angle the rope makes with the pole
(the rope, radius and pole form a right angled triangle):

tan(angle) = centre force / weight

= mv^2/R / mg

= v^2/(gR)

**Angle = arctan(v^2/(gR) )**

**= arctan( 5.0^2 /(9.81* 1.0) )**

**= 68.57 degrees**

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?

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...

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 148 g ball is tied to a string. It is pulled to an angle of
7.2 ∘ and released to swing as a pendulum. A student with a
stopwatch finds that 22 oscillations take 20 s .

the figure shows a 3.0 kg ball tied to the end of a 50 cm long
string being swung in a circle in a vertical plane at constant
speed. The center of the circle is h = 230 cm above the floor. The
ball is swung at the minimum speed necessary to make it over the
top without the string going slack. If the string is released at
the instant the ball is at the top of the loop, how...

A 300g rock tied to a string is rotated in a vertical circle (up
and down, so gravity is important) with radius 0.5m. Model the rock
as a point particle. If a torque of 2Nm is applied for 3s, what is
the rotation rate of the rock? What is the tension in the string at
the top of the circle?

A small ball of mass ? is attached to the bottom end a light
string of length ?, while the top of the string is fixed to the
ceiling. If the ball is moving in a horizontal circle of radius ?,
derive an expression for the angular speed ? of the ball in terms
of only ?, ?, ? and ?. Such a system is called a conical
pendulum.

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...

If
a stone is tied to one end of the string and whirled in vertical
circle such that it rotates with constant speed, then the tension
in the string is minimum at

A ball on the end of a string is whirled around in a horizontal
circle of radius 0.340 m. The plane of the circle is 1.50 m above
the ground. The string breaks and the ball lands 1.50 m
(horizontally) away from the point on the ground directly beneath
the ball's location when the string breaks. Find the radial
acceleration of the ball during its circular motion.
Magnitude
m/s2Direction
away from the center of curvature
toward the center of curvature

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 50 seconds ago

asked 10 minutes ago

asked 14 minutes ago

asked 16 minutes ago

asked 31 minutes ago

asked 42 minutes ago

asked 48 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago