Answer:
5 miles per hour
Explanation:
if you divide 15 by 3 you get 5, therefore the student is going 5 miles per hour.
Answer:
the net toque is τ=8.03* 10⁻⁴ N*m
Explanation:
Assuming the disk has constant density ρ, the moment of inertia I of is
I = ∫r² dm
since m = ρ*V = ρπR² h , then dm= 2ρπh r dr
thus
I = ∫r²dm = ∫r²2ρπh r dr =2ρπh ∫r³ dr = 2ρπh (R⁴/4- 0⁴/4)= ρπhR⁴ /2= mR²/2
replacing values
I = mR²/2= 0.017 kg * (0.06 m)²/2 = 3.06 *10⁻⁵ kg*m²
from Newton's second law applied to rotational motion
τ= Iα , where τ=net torque and α= angular acceleration
since the angular velocity ω is related with the angular acceleration through
ω= ωo + α*t → α =(ω-ωo)/t = (21 rad/s-0)/0.8 s = 26.25 rad/s²
therefore
τ= Iα= 3.06 *10⁻⁵ kg*m²*26.25 rad/s² = 8.03* 10⁻⁴ N*m
Construct a vector diagram. It will be a right-angled triangle. One vector (the hypotenuse) represents the heading of the boat, one represents the current and one represents the resultant speed of the boat, which I'll call x. Their magnitudes are 20, 3 and x. Let the required angle = theta. We have:
<span>theta = arcsin(3/20) = approx. 8.63° </span>
<span>The boat should head against the current in a direction approx. 8.63° to the line connecting the dock with the point opposite, or approx. 81.37° to the shore line. </span>
<span>x = sqrt(20^2 - 3^2) </span>
<span>= sqrt(400 - 9) </span>
<span>= sqrt 391 </span>
<span>The boat's crossing time = </span>
<span>0.5 km/(sqrt 391 km/hr) </span>
<span>= (0.5/sqrt 391) hr </span>
<span>= approx. 0.025 hr </span>
<span>= approx. 91 seconds</span>
Answer: 6.36
Explanation:
Given
Radius of grindstone, r = 4 m
Initial angular speed of grindstone, w(i) = 8 rad/s
Final angular speed of the grindstone, w(f) = 12 rad/s
Time used, t = 4 s
Angular acceleration of the grinder,
α = Δw / t
α = w(f) - w(i) / t
α = (12 - 8) / 4
α = 4/4 = 1 rad/s²
Number of complete revolution in 4s =
Δθ = w(i).t + 1/2.α.t²
Δθ = 8 * 4 + 1/2 * 1 * 4²
Δθ = 32 + 1/2 * 16
Δθ = 32 + 8
Δθ = 40 rad/s
40 rad/s = 40/2π rpm = 6.36 rpm
Therefore, the grindstone does 6.36 revolutions during the 4 s interval
After reading this whole question, I feel like I've already
earned 5 points !
-- Two satellites at the same distance, different masses:
The forces of gravity between two objects are directly
proportional to the product of the objects' masses. In
other words, the gravitational forces between the Earth
and an object on its surface are proportional to the mass of
the object. In other words, people with more mass weigh more
on the Earth, and the Earth weighs more on them.
If the satellites are both at the same distance from Earth,
then the Earth pulls on the one with more mass with greater
force, and also the one with more mass pulls on the Earth
with greater force.
-- Two satellites with the same mass, at different distances:
The forces of gravity between two objects are inversely
proportional to the square of the distance between them.
In other words, the gravitational
forces between the Earth
and an object are inversely proportional
to the square of
the distance between the object and the center of the Earth.
If
the satellites both have the same mass, then the Earth
pulls on the nearer one with greater force, and also the
nearer one pulls on the Earth with greater force.
-- Resistor in a circuit when the voltage changes:
The resistance depends on how the resistor was manufactured.
Its resistance is marked on it, and doesn't change. It remains
the same whether the voltage changes, the current changes,
the time of day changes, the cost of oil changes, etc.
If you increase the voltage in the circuit where that resistor is
installed, the current through the resistor increases. If the current
remains constant, then you can be sure that somebody snuck over
to your circuit when you weren't looking, and they either installed
another resistor in series with the original one to make the total
resistance bigger, or else they snipped the original one out of the
circuit and quickly connected one with more resistance in its place.
