Question

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 2^{nd} 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, we
will take the z axis to be the vertical direction. The weight w =
mg is in the downward z direction, while the tension T is in the
upward direction of the string. The vector sum of these forces
should be set equal to the mass times the acceleration of the ball,
but that is zero in this case.

2. Horizontal circular motion The ball is now set into circular
motion with a constant velocity v = 2.00 m/s and radius r = 0.300 m
in the horizontal xy plane. Draw arrows showing the forces acting
on the ball, and the direction of the centripetal acceleration.
Compute the magnitude of the acceleration, and also the period
T_{p} of the motion (the time for one complete revolution
around the circle).

3. To find the angle φ corresponding to the given velocity and
radius we need to consider the x and z components of the forces in
question 2, separately. Since there is no motion in the z
direction, the acceleration a_{z} = 0. Hence the sum of the
z components of the forces must be equal to zero. From this, solve
for an equation relating the tension force in the string to the
angle φ.

4. Take the x axis to be centered on the ball, and pointing
radially inward toward the center of the circle. Newton’s
2^{nd} law now states that the sum of the x components of
the forces in question 2 must be equal to the mass times the
centripetal acceleration. Solve this equation for the tension force
in the string, and since this must be equal to the equation you
found in slide 4, find an equation relating the angle φ to the
velocity and radius. Calculate φ for the values given on question 2
, and then from the equation for

T on question 2 find the tension in the string for the rotating
ball .

5. Vertical circular motion The ball is now set into circular motion in an xz plane perpendicular to the ground. In the drawing below, draw and label arrows showing the forces acting on the ball at the four different positions around the circle. Also show the net acceleration direction at each position (adding the vectors for the gravitational acceleration and the centripetal acceleration). The ball will slow down going up, and speed up coming down, shown by the velocity arrows in the drawing.

Answer #1

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...

1. An object of mass 1.2 kg is attached to a string of 0.83 m.
When this object is rotated around a horizontal circle, it
completes 15 revolutions in 9.6 seconds.
a. What is the period (T) of this motion?
b. What is the tangential velocity of the object?
c. What is the tension on the string? Hint: The tension on the
string is the centripetal force that causes the circular
motion.

A small ball of mass 61 g is suspended from a string of length
62 cm and whirled in a circle lying in the horizontal plane. If the
string makes an angle of 25◦ with the vertical, find the
centripetal force experienced by the ball. The acceleration of
gravity is 9.8 m/s 2 . Answer in units of N

Hanging from the rear view mirror of your car is a plastic
soccer ball. The ball is hanging from a single string. While making
a right turn at 45 mph, you notice that the angle the ball and
string make from the vertical is precisely 33◦.
(a) Illustrate and fully label the situation described
above.
(b) Construct a Free Body Diagram of the soccer ball during the
turn.
C) Determine the radius of the circular path of the soccer ball...

Question 1
The study of Uniform Circular Motion relates to objects
traveling with constant speed around a circle with radius, R. Since
the object has a constant speed along a circular path, we can also
say that
A)
the object has zero velocity.
B)
the object has a constant acceleration magnitude.
C)
the object has zero acceleration.
D)
the object has a constant velocity.
E)
the object has an increasing acceleration.
Question 2
Uniform Circular Motion (UCM) problems are just...

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

A 10-kg mass is hanging exactly at the center of a string. The
strong guy is holding the string at rest, such that the angle is ?
= 15∘.
(a) Determine the Tension forces F1 and F2 on the
string.
(b) Can the strong guy exert a force to keep the string
perfectly horizontal? Explain your answer

A mass of 4.83 kg is suspended from a 1.91 m long string. It
revolves in a horizontal circle. If the string makes an angle of
56.9 degrees with the vertical, then what is the net force acting
on the mass?

-According to Newton’s First Law, which of the following
statements is true?
a) If an object is in motion, then a force is acting on it.
b) A force is necessary to change the motion of an object.
c) If an object is stationary, then no forces are acting on
it.
d) An object in motion must have an acceleration.
-If an object is in motion, can its acceleration be zero?
-If an object’s acceleration is zero, does that mean...

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?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 21 minutes ago

asked 32 minutes ago

asked 33 minutes ago

asked 39 minutes ago

asked 47 minutes ago

asked 52 minutes ago

asked 52 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago