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
vova2212 [387]
3 years ago
5

A ball filled with an unknown material starts from rest at the top of a 2 m high incline that makes a 28o with respect to the ho

rizontal. The ball rolls without slipping down the incline and at the bottom has a speed of 4.9 m/s. How many revolutions does the ball rotate through as it rolls down the incline
Physics
1 answer:
Lady_Fox [76]3 years ago
3 0

Answer:

<u>Searching in google I found the total mass and the radius of the ball (m = 1.5 kg and r = 10 cm) which are needed to solve the problem!</u>  

The ball rotates 6.78 revolutions.

     

Explanation:

<u>Searching in google I found the total mass and the radius of the ball (m = 1.5 kg and r = 10 cm) which are needed to solve the problem!</u>        

At the bottom the ball has the following angular speed:

\omega_{f} = \frac{v_{f}}{r} = \frac{4.9 m/s}{0.10 m} = 49 rad/s

Now, we need to find the distance traveled by the ball (L) by using θ=28° and h(height) = 2 m:

sin(\theta) = \frac{h}{L} \rightarrow L = \frac{h}{sin(\theta)} = \frac{2 m}{sin(28)} = 4.26 m

To find the revolutions we need the time, which can be found using the following equation:                

v_{f} = v_{0} + at  

t = \frac{v_{f} - v_{0}}{a} (1)

So first, we need to find the acceleration:

v_{f}^{2} = v_{0}^{2} + 2aL \rightarrow a = \frac{v_{f}^{2} - v_{0}^{2}}{2L}    (2)  

By entering equation (2) into (1) we have:

t = \frac{v_{f} - v_{0}}{\frac{v_{f}^{2} - v_{0}^{2}}{2L}}

Since it starts from rest (v₀ = 0):  

t = \frac{2L}{v_{f}} = \frac{2*4.26 m}{4.9 m/s} = 1.74 s

Finally, we can find the revolutions:  

\theta_{f} = \frac{1}{2} \omega_{f}*t = \frac{1}{2}*49 rad/s*1.74 s = 42.63 rad*\frac{1 rev}{2\pi rad} = 6.78 rev

Therefore, the ball rotates 6.78 revolutions.

I hope it helps you!                                                                                                                                                                                          

You might be interested in
What force is needed to accelerate 300kg rock as a rste of 4m/s​
Natali [406]

Answer:

60 maybe

Explanation:

4 0
3 years ago
Read 2 more answers
Why are stars considered to be the building blocks of the universe?
eduard
The answer for that would be C
4 0
3 years ago
Read 2 more answers
The BMI of someone that weights 121 pounds and is 64 inches tall:
nordsb [41]

Answer:

B

;)

Explanation:

8 0
3 years ago
Read 2 more answers
I just need x isolated
mamaluj [8]

Answer:

x=\frac{-y+\sqrt{y^2+4rt} }{2r}

x=\frac{-y-\sqrt{y^2+4rt} }{2r}

Explanation:

rx+y=\frac{t}{x}\\\\x(rx+y)=(\frac{t}{x})x\\\\rx^2+yx=t\\\\rx^2+yx-t=t-t\\\\rx^2+yx-t=0

Solve using the quadratic formula.

x=\frac{-y+\sqrt{y^2+4rt} }{2r}

x=\frac{-y-\sqrt{y^2+4rt} }{2r}

7 0
3 years ago
Read 2 more answers
What is terrestrial radiation?
Feliz [49]
C) Radiation that comes from Earth...... Hope it helps, Have a nice day :)
6 0
3 years ago
Read 2 more answers
Other questions:
  • Three different planet-star systems, which are far apart from one another, are shown above. The masses of the planets are much l
    15·1 answer
  • A paratrooper is initially falling downward at a speed of 27.6 m/s before her parachute opens. When it opens, she experiences an
    6·1 answer
  • An object of mass m moves in one dimension with velocity given by v a/x for a a constant. Find the force on the object as a func
    10·1 answer
  • would you expect the air pressure in a valley thats below sea level to be higher or lower than the air pressure at sea level
    5·1 answer
  • A pulley with a radius of 3.0 cm and a rotational inertia of 4.5 x 10^-3 kg∙m2 is suspended from the ceiling. A rope passes over
    10·1 answer
  • Explain how to identify a starting position<br> on a line.
    6·1 answer
  • c) If the ice block (no penguins) is pressed down even with the surface and then released, it will bounce up and down, until fri
    10·1 answer
  • The mass of the earth is 5.96/10kg^24. The radius of the earth is approximately 6.37x10^6 calculate the force of gravity
    10·1 answer
  • An electric heater is madde of a wire of resistance 100π and connected to a 240v mains supply. Determine the power rating of the
    15·1 answer
  • Chimneys don't get smoke in the house because of...?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!