A sphere with a radius of 15 cm rolls on a level surface with a constant angular speed of 10 rad/s. To what height on a 30° incl
ined plane will the sphere roll before coming to rest? (Neglect frictional losses.) [ 0.16 m]
1 answer:
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Answer:
B) waves speed up
C) waves bend away from the normal
Explanation:
The index of refraction of a material is the ratio between the speed of light in a vacuum and the speed of light in that medium:
where
c is the speed of light in a vacuum
v is the speed of light in the medium
We can re-arrange this equation as:
So from this we already see that if the index of refraction is lower, the speed of light in the medium will be higher, so one correct option is
B) waves speed up
Moreover, when light enters a medium bends according to Snell's Law:
where
are the index of refraction of the 1st and 2nd medium
are the angles made by the incident ray and refracted ray with the normal to the interface
We can rewrite the equation as
So we see that if the index of refraction of the second medium is lower (), then the ratio
is larger than 1, so the angle of refraction is larger than the angle of incidence:
This means that the wave will bend away from the normal. So the other correct option is
C) waves bend away from the normal
Answer:
Explanation:
Given that,
Mass, m = 27 grams
Volume of the substance, V = 15 cm³
We need to find the density of the substance. We know that, the density of an object is given by mass per unit volume. So,
So, the density of the substance is equal to .
Answer:
ω = 2.1 rad/sec
Explanation:
- As the rock is moving along with the merry-go-round, in a circular trajectory, there must be an external force, keeping it on track.
- This force, that changes the direction of the rock but not its speed, is the centripetal force, and aims always towards the center of the circle.
- Now, we need to ask ourselves: what supplies this force?
- In this case, the only force acting on the rock that could do it, is the friction force, more precisely, the static friction force.
- We know that this force can be expressed as follows:
where μs = coefficient of static friction between the rock and the merry-
go-round surface = 0.7, and Fn = normal force.
- In this case, as the surface is horizontal, and the rock is not accelerated in the vertical direction, this force in magnitude must be equal to the weight of the rock, as follows:
- Fn = m*g (2)
- This static friction force is just the same as the centripetal force.
- The centripetal force depends on the square of the angular velocity and the radius of the trajectory, as follows:
- Since (1) is equal to (3), replacing (2) in (1) and solving for ω, we get:
- This is the minimum angular velocity that would cause the rock to begin sliding off, due to that if it is larger than this value , the centripetal force will be larger that the static friction force, which will become a kinetic friction force, causing the rock to slide off.