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
You apply the brakes of your car abruptly and your book starts sliding off the front seat. Three observers sitting in the car ex
krek1111 [17]

Answer:

All the observers are correct.

Explanation:

This is simply a problem of reference frames from which the motion of the book is being viewed by the various observers.

From their various reference frames, they are all correct.

Observer A must be in the inertial reference frame.

<em>Observers who can explain the behavior of the book  and the car by using the relationship between the sum of  the forces and changing velocity are said to be observers in inertial reference frames.</em>

This is clearly shown by what observer A noticed. There was a relative motion between the book and the car as she pointed out, making her to be in an inertial reference frame.

<em>Similarly, observers in inertial reference frames can also explain the changes in velocity of objects  by considering the forces exerted on them by other objects.</em>

This is shown by observer B as he is able to notice how the force of the car affects the velocity of the book.

Observer C is actually in a non-inertial reference frame, as newtons law of force motion relationship are no longer observed. This occurs in the non inertial reference frame.

7 0
3 years ago
Determine the acceleration of a pendulum bob as it passes through an angle of 15 degrees to the right of the equilibrium point.
BigorU [14]

Answer:

Explanation:

Since energy is conserved:

2

mu  

2

 

​

=  

2

mv  

2

 

​

+mgh

⇒u  

2

=v  

2

+2gh

⇒(3)  

2

=v  

2

+2(9.8)(0.5−0.5cos60)

⇒v=2m/s

7 0
3 years ago
Calculate the kinetic energy of a 0.032 kg ball as it leaves a hand to be thrown upwards at 6.2 m/s
AnnZ [28]

Answer:

The ball will have a kinetic energy of 0.615 Joules.

Explanation:

Use the kinetic energy formula

E_k = \frac{1}{2}mv^2 = \frac{1}{2}0.032kg\cdot 6.2^2 \frac{m^2}{s^2}= 0.615J

The kinetic energy at the moment of leaving the hand will be 0.615 Joules. (From there on, as it ball is traveling upwards, this energy will be gradually traded off with potential energy until the ball's velocity becomes zero at the apex of the flight)

3 0
3 years ago
In a clear cup there are three substances. Their densities are 3, 1, and 2. From top of the cup to the bottom, what would the or
Vesnalui [34]

Answer:

1, 2 and 3

Explanation:

The most dense substance will settle at the bottom of the cup

4 0
2 years ago
Question 9:<br> All parts thank you !
WINSTONCH [101]
Photo Math is the answer
5 0
3 years ago
Other questions:
  • 17. A skateboard has a mass of 3.2 kg. If it slips out from a skateboarder and has
    13·1 answer
  • Suppose that you wanted to close a door by throwing a ball at the door. one ball will bounce off the door in a perfectly elastic
    7·1 answer
  • If the<br> refractive index of benzere is 2.419,<br> what is the speed of light in benzene?
    12·1 answer
  • 4. The place on a magnet where the magnet exerts the strongest magnetic force
    8·1 answer
  • A concave mirror forms a real image at 15.0 cm from the mirror surface along the principal axis. If the corresponding object is
    8·1 answer
  • Which of the following changes occurs during nuclear fission?
    14·1 answer
  • The 360-turn primary coil of a step-down transformer is connected to an ac line that is 120 V (rms). The secondary coil is to su
    12·1 answer
  • Two point charges, the first with a charge of 4.47 x 10-6 C and the second with a charge of 1.86 x 10-6 C, are separated by 17.4
    11·2 answers
  • How are frequency and were peroid related?
    6·1 answer
  • Due in 30 help me please ​
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!