Answer:
A) a = 73.304 rad/s²
B) Δθ = 3665.2 rad
Explanation:
A) From Newton's first equation of motion, we can say that;
a = (ω - ω_o)/t. We are given that the centrifuge spins at a maximum rate of 7000rpm.
Let's convert to rad/s = 7000 × 2π/60 = 733.04 rad/s
Thus change in angular velocity = (ω - ω_o) = 733.04 - 0 = 733.04 rad/s
We are given; t = 10 s
Thus;
a = 733.04/10
a = 73.304 rad/s²
B) From Newton's third equation of motion, we can say that;
ω² = ω_o² + 2aΔθ
Where Δθ is angular displacement
Making Δθ the subject;
Δθ = (ω² - ω_o²)/2a
At this point, ω = 0 rad/s while ω_o = 733.04 rad/s
Thus;
Δθ = (0² - 733.04²)/(2 × 73.304)
Δθ = -537347.6416/146.608
Δθ = - 3665.2 rad
We will take the absolute value.
Thus, Δθ = 3665.2 rad
The center of mass is given with this formula:
Velocity is:
So, for the velocity of the center of mass we have:
In our case it is:
I believe the answer is B. that's where the asetroid belt is.
Answer:
Explanation:
<u>Simple Pendulum</u>
It's a simple device constructed with a mass (bob) tied to the end of an inextensible rope of length L and let swing back and forth at small angles. The movement is referred to as Simple Harmonic Motion (SHM).
(a) The angular frequency of the motion is computed as
We have the length of the pendulum is L=0.81 meters, then we have
(b) The total mechanical energy is computed as the sum of the kinetic energy K and the potential energy U. At its highest point, the kinetic energy is zero, so the mechanical energy is pure potential energy, which is computed as
where h is measured to the reference level (the lowest point). Please check the figure below, to see the desired height is denoted as Y. We know that
And
Solving for Y
The potential energy is
The mechanical energy is, then
(c) The maximum speed is achieved when it passes through the lowest point (the reference for h=0), so the mechanical energy becomes all kinetic energy (K). We know
Equating to the mechanical energy of the system (M)
Solving for v
A 300-kg bear grasping a vertical tree slides down at constant velocity. The friction force between the
tree and the bear is