A solid, uniform sphere of mass 2.0 kg and radius 1.8 m rolls from rest without slipping down an inclined plane of height 7.5 m. What is the angular velocity of the sphere at the bottom of the inclined plane

Answers

Answer 1

Answer:

[tex]w^2=5.5rads/s[/tex]

Explanation:

From the question we are told that:

Mass [tex]m=2.0kg[/tex]

Radius [tex]r=1.8m[/tex]

Height [tex]h=7.5m[/tex]

Generally the equation for Potential energy is mathematically given by

Potential energy=Kinetic energy+Rotational energy

 [tex]mgh=\frac{1}{2}mv^2+\frac{1}{2}Iw^2[/tex]

Since there is no slipping

 [tex]v=rw[/tex]

Therefore

 [tex]mgh=\frac{1}{2}mr^2w^2+\frac{1}{2}Iw^2[/tex]

Where

      [tex]I=\frac{1}{2}mr^2[/tex]

      [tex]l=3.24m[/tex]

 [tex]2*9.81*7.5=\frac{1}{2}(2)(1.8)^2w^2+\frac{1}{2}(3.24)w^2\\\\[/tex]

 [tex]147.15=3.24w^2+1.62w^2[/tex]

 [tex]w^2=\frac{147.15}{4.86}[/tex]

 [tex]w^2=\sqrt{\frac{147.15}{4.86}}[/tex]

 [tex]w^2=5.5rads/s[/tex]


Related Questions

Explain the mode of operation of x-ray​

Answers

Answer:

If x-rays get in touch with our body tissues, they create a picture of a metal film. The high energizing rays are unable to penetrate soft tissue, such as skin and organs and travel through the laser. The places where the x-rays pass soft tissues are Black areas of an X-ray.

Answer:

Explanation:

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Any is 160 cm tall and stands 50 cm in front of a plane mirror. The image of Amy is ?

Answers

Answer:

Option A. 160 cm tall and 100 cm in front of Amy

Explanation:

To know the the correct answer to the question, we must recognise that the image formed by plane mirror is:

I. Same size as the object.

II. Same distance as the object from the mirror.

III. Laterally inverted.

IV. Virtual

With the above information, we obtained the answer to the question as follow:

Object height = 160 m

Thus,

Image height = 160 m

Distance of object from mirror = 50 cm

Therefore,

Distance of image from the mirror = 50 cm

Distance between the object and image = 50 + 50 = 100 cm

Thus, option A gives the correct answer to the question because the image of Amy is 160 cm tall and 100 cm in front of her.

If the frequency of a wave is doubled, what happens to that waves energy

Answers

Answer:

If the frequency of a wave is doubled, what happens to its wavelength? If the frequency is doubled, the wavelength is only half as long. 3. ... As the frequency slows down, the wavelength increases.

Explanation:

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