Answer:
Part(a): The angular acceleration is .
Part(b): The angular displacement is .
Explanation:
Part(a):
If be the initial angular speed, final angular speed and angular acceleration of the centrifuge respectively, then from rotational kinematic equation, we can write
where '' is the time taken by the centrifuge to increase its angular speed.
Given, ,
and
. From equation (
), the angular acceleration is given by
Part(b):
Also the angular displacement () can be written as
Answer:
μs = 0.36
Explanation:
Assuming no other forces acting on the cup while the car is decelerating, the friction force is responsible for any horizontal movement of the cup.
If the cup is on the verge of starting to slide, the friction force can be expressed as follows:
Ff = -μs*N = -μs*m*g
This force produces a deceleration from 45 Kmh to rest, in 3.5 s or more.
Converting 45 kmh to m/s, we have:
We can find the acceleration, just applying the definition, with vf =0, as follows:
According to Newton's 2nd law, we can write the following expression:
F = m*a = -μs*m*g
Simplifying common terms, we can solve for μs, as follows:
μs =