Answer:
a) α = 0.338 rad / s² b) θ = 21.9 rev
Explanation:
a) To solve this exercise we will use Newton's second law for rotational movement, that is, torque
τ = I α
fr r = I α
Now we write the translational Newton equation in the radial direction
N- F = 0
N = F
The friction force equation is
fr = μ N
fr = μ F
The moment of inertia of a saying is
I = ½ m r²
Let's replace in the torque equation
(μ F) r = (½ m r²) α
α = 2 μ F / (m r)
α = 2 0.2 24 / (86 0.33)
α = 0.338 rad / s²
b) let's use the relationship of rotational kinematics
w² = w₀² - 2 α θ
0 = w₀² - 2 α θ
θ = w₀² / 2 α
Let's reduce the angular velocity
w₀ = 92 rpm (2π rad / 1 rev) (1 min / 60s) = 9.634 rad / s
θ = 9.634 2 / (2 0.338)
θ = 137.3 rad
Let's reduce radians to revolutions
θ = 137.3 rad (1 rev / 2π rad)
θ = 21.9 rev
Answer:
C
Explanation:
Exercise also increases your levels of HDL cholesterol, the "good" cholesterol that lowers heart disease risk by flushing the artery-clogging LDL or "bad" cholesterol out of your system.
Answer:
What constant velocity means
Explanation:
To have a constant velocity, an object must have a constant speed in a constant direction
Explanation:
gravitational potential energy = mgh (must be in S.I. unit)
m= 0.4 kg ; g= 10m/s (gravitational acceleration occurs); h=9.2 m
hence mgh=0.4×10×9.2= 36.8J
unit for energy is joules and since the variables are in S.I. unit, we can use Joules as the final unit for measurement
<span>Suppose the pipe goes underwater directly from the resort to point P, which is x miles away from the point on the shoreline that's closest to the resort.
By Pythagoras, the distance from the resort to P is: sqrt(x^2 + 3^2) = sqrt(x^2 + 9)
Suppose that it costs 1 unit of money per mile to lay pipe on land, so therefore it costs 1.5 units of money to lay pipe underwater. So the cost of the pipe above is: 1.5*sqrt(x^2 + 9)
So the distance from P to the fresh water source is 10 - x, so the cost of laying that pipe is 10 - x.
Total cost of pipe: C = 1.5*sqrt(x^2 + 9) + 10 - x
dC/dx = ((1.5x) / sqrt(x^2 + 9)) - 1
To minimize C, set the derivative to zero:
((1.5x) / sqrt(x^2 + 9)) - 1 = 0
(1.5x) / sqrt(x^2 + 9) = 1
1.5x = sqrt(x^2 + 9)
(1.5x)^2 = x^2 + 9
2.25x^2 = x^2 + 9
2.25x^2 - x^2 = 9
1.25x^2 = 9
x^2 = 9 / 1.25
x = sqrt(9/1.25)
x = 2.683</span>
