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.
Complete Question:
A beam of light from a monochromatic laser shines into a piece of glass. The glass has thickness Land index of refraction n=1.5. The wavelength of the laser light in vacuum is L/10 and its frequency is f. In this problem, neither the constant c nor its numerical value should appear in any of your answers.
How long does it take for a short pulse of light to travel from one end of the glass to the other?
Express your answer in terms of the frequency, f. Use the numeric value given for n in the introduction.
Answer:
15/f
Explanation:
Wavelength of the laser light, λ = L/10
Where L = Distance covered by the light
Refractive index, n = 1.5
Speed, v = λf
Since we are considering the laser light, the speed of light, c, will be used.
c = v
c = λf
c = (L/10)f
(L/10)f = L/t
f/10 = 1/t
t = 10/f
since the refractive index, n = 1.5
t = 1.5(10/f)
t = 15/f
Answer:
a=12 m/s²
Explanation:
Newton's second law of motion states that the acceleration of a body is directly proportional to the force applied and takes place in the direction of force.
This can be summarized as: F=ma, where m is the mass of the object on which force F acts. a is the acceleration due to the force applied.
12N= 1kg×a
a=12N/1kg
a=12m/s²
use F = ma
F : force m : mass a : acceleration
so
f = 5kg * 20 m/s2 = 100 N