Answer:
Part a)
Part b)
Part c)
Part d)
Explanation:
Part a)
While bucket is falling downwards we have force equation of the bucket given as
for uniform cylinder we will have
so we have
now we have
now we have
Part b)
speed of the bucket can be found using kinematics
so we have
Part c)
now in order to find the time of fall we can use another equation
Part d)
as we know that cylinder is at rest and not moving downwards
so here we can use force balance
Answer:
The angular acceleration of the pencil<em> α = 17 rad·s⁻²</em>
Explanation:
Using Newton's second angular law or torque to find angular acceleration, we get the following expressions:
τ = I α (1)
W r = I α (2)
The weight is that the pencil has is,
sin 10 = r / (L/2)
r = L/2(sin(10))
The shape of the pencil can be approximated to be a cylinder that rotates on one end and therefore its moment of inertia will be:
I = 1/3 M L²
Thus,
mg(L / 2)sin(10) = (1/3 m L²)(α)
α(f) = 3/2(g) / Lsin(10)
α = 3/2(9.8) / 0.150sin(10)
<em> α = 17 rad·s⁻²</em>
Therefore, the angular acceleration of the pencil<em> </em>is<em> 17 rad·s⁻²</em>
Answer:
1500 mph
Explanation:
Take east to be +x and north to be +y.
The x component of the velocity is:
vₓ = 889 cos 0° + 830 cos 59°
vₓ = 1316.5 mph
The y component of the velocity is:
vᵧ = 889 sin 0° + 830 sin 59°
vᵧ = 711.4 mph
The speed is found with Pythagorean theorem:
v² = vₓ² + vᵧ²
v² = (1316.5 mph)² + (711.4 mph)²
v = 1496 mph
Rounded to two significant figures, the jet's speed relative to the ground is 1500 mph.
Decreased it because you can float a lot
Answer:
The answer is below
Explanation:
A diver works in the sea on a day when the atmospheric pressure is 101 kPa. The diver uses compressed air to breathe under water. 1700 litres of air from the atmosphere is compressed into a 12-litre gas cylinder. The compressed air quickly cools to its original temperature. Calculate the pressure of the air in the cylinder.
Solution:
Boyles law states that the volume of a given gas is inversely proportional to the pressure exerted by the gas, provided that the temperature is constant.
That is:
P ∝ 1/V; PV = constant
P₁V₁ = P₂V₂
Given that P₁ = initial pressure = 101 kPa, V₁ = initial volume = 1700 L, P₂ = cylinder pressure, V₂ = cylinder volume = 12 L. Hence:
P₁V₁ = P₂V₂
100 kPa * 1700 L = P₂ * 12 L
P₂ = (100 kPa * 1700 L) / 12 L
P₂ = 14308 kPa