1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
mr Goodwill [35]
3 years ago
14

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

8 kg and moves at v = 5.22 m/s. The circular path has a radius of R = 1.1 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 ball is at the side of the circle? . 3) What is the magnitude of the tension in the string when the ball is at the top of the circle? 4) What is the minimum velocity so the string will not go slack as the ball moves around the circle?
Physics
1 answer:
Oksanka [162]3 years ago
7 0

1) 5.5 N

When the ball is at the bottom of the circle, the equation of the forces is the following:

T-mg = m\frac{v^2}{R}

where

T is the tension in the string, which points upward

mg is the weight of the string, which points downward, with

m = 0.158 kg being the mass of the ball

g = 9.8 m/s^2 being the acceleration due to gravity

m \frac{v^2}{R} is the centripetal force, which points upward, with

v = 5.22 m/s being the speed of the ball

R = 1.1 m being the radius of the circular trajectory

Substituting numbers and re-arranging the formula, we find T:

T=mg+m\frac{v^2}{R}=(0.158 kg)(9.8 m/s^2)+(0.158 kg)\frac{(5.22 m/s)^2}{1.1 m}=5.5 N

2) 3.9 N

When the ball is at the side of the circle, the only force acting along the centripetal direction is the tension in the string, therefore the equation of the forces becomes:

T=m\frac{v^2}{R}

And by substituting the numerical values, we find

T=(0.158 kg)\frac{(5.22 m/s)^2}{1.1 m}=3.9 N

3) 2.3 N

When the ball is at the top of the circle, both the tension and the weight of the ball point downward, in the same direction of the centripetal force. Therefore, the equation of the force is

T+mg=m\frac{v^2}{R}

And substituting the numerical values and re-arranging it, we find

T=m\frac{v^2}{R}-mg=(0.158 kg)\frac{5.22 m/s)^2}{1.1 m}-(0.158 kg)(9.8 m/s^2)=2.3 N

4) 3.3 m/s

The minimum velocity for the ball to keep the circular motion occurs when the centripetal force is equal to the weight of the ball, and the tension in the string is zero; therefore:

T=0\\mg = m\frac{v^2}{R}

and re-arranging the equation, we find

v=\sqrt{gR}=\sqrt{(9.8 m/s^2)(1.1 m)}=3.3 m/s

You might be interested in
If the coefficient of friction is 0.3900 and the cylinder has a radius of 2.700 m, what is the minimum angular speed of the cyli
Aleks04 [339]

Answer:

w=3.05 rad/s or 29.88rpm

Explanation:

k = coefficient of friction = 0.3900

R = radius of the cylinder = 2.7m

V = linear speed of rotation of the cylinder

w = angular speed = V/R or to rewrite V = w*R

N = normal force to cylinder

N==\frac{m(V)^{2}}{R}=m*(w)^2*R

Friction force\\Ff = k*N\\Ff= k*m*w^2*R

Gravitational force \\Fg = m*g

These must be balanced (the net force on the people will be 0) so set them equal to each other.

Fg = Ff

m*g = k*m*w^2*R

g=k*w^{2}*R

w^2 =\frac{g}{k*R}

w=\sqrt{\frac{g}{k*R}} \\w =\sqrt{\frac{9.8\frac{m}{s^{2}}}{0.3900*2.7m}}\\ w=\sqrt{9.306}=3.05 \frac{rad}{s}

There are 2*pi radians in 1 revolution so:

RPM=\frac{w}{2\pi }*60\\RPM=\frac{3.05\frac{rad}{s}}{2\pi}*60\\RPM= 0.498*60\\RPM=29.88

So you need about 30 RPM to keep people from falling out the bottom

7 0
3 years ago
Which of the following statements best describes the second law of
Serga [27]

Answer:

B

Explanation:

Heat flows from hot to cold to lower the temperature of hot areas and increase temperature of cold areas. The end result is that the 2 areas have the same temperature, thus increasing entropy.

7 0
3 years ago
A body of mass 5 kg has a velocity<br><br><br>20 MS <br><br>-1 its Momentum is​
Anon25 [30]

Answer:

Momentum is 100 kg.m/s

Explanation:

given

mass, m = 5 kg

velocity, v = 20 m/s

To find : momentum (P)

We know that momentum is given by equation:

p = mv

  = 5 kg x 20 m/s

  = 100 kg.m/s

7 0
3 years ago
(b) Which has more mass: 50 cm of gold or 50 cm of aluminum? Explain.
monitta
Gold’s molar mass is about 196 while aluminum is about 27, thus 50cm of gold has more mass
8 0
3 years ago
How does a substance's temperatura chanté when the average kinetic energy of its particles increases? When it decreases?
Aleks [24]
Kinetic energy means movement. This means that the more something moves, the more kinetic energy it will have! And the faster something moves, the more heat it produces! Altogether, this means that the more Kinetic energy something has, the hotter it will be!

The opposite is also true. The less something moves, it will have less Kinetic energy and the colder it will get. 

If you're having trouble understanding this, think of it like how the particles in water move compared to how the particles in ice move. The particles in water are free flowing and can move wherever they want. If they get colder, they won't move as much, and eventually they'll stop flowing around, forming a solid and staying colder than the water will get.
7 0
3 years ago
Other questions:
  • While wearing rubber-soled shoes, you rub a helium balloon on your sweater. the balloon becomes negative charged. now release th
    9·1 answer
  • Find the magnitude of the resultant force and the angle it makes with the positive x-axis. (Let a = 200 N and b = 400 N. Round y
    12·1 answer
  • The three types of stress that act on Earth's rocks are compression, tension, and
    6·1 answer
  • Find the magnitude of the sum
    9·1 answer
  • Each of 100 identical blocks sitting on a frictionless surface is connected to the next block by a massless string. The first bl
    10·1 answer
  • how would the tides on earth be different if the moon revolved around the earth in 15 days instead of 30 days
    11·1 answer
  • Which car has the most kinetic energy?
    12·1 answer
  • A computer simulation is an example of what?
    6·1 answer
  • How will doctors most likely respond to someone who has an active case of drug-resistant tuberculosis?
    7·1 answer
  • What is the term used when a ball is hit and the batter reaches the following bases safely (without being called out)?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!