1) The terminal velocity of a 4×10^−5 kg raindrop is about 5 m/s . Assuming a drag force Fd= -bv.
A) Assuming a drag force determine the value of the constant b.
B) Assuming a drag force determine the time required for such a drop, starting from rest, to reach 63% of terminal velocity.
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The drag force is negative because it causes the velocity of a falling object to decrease.
The rain drop has two vertical forces which affect its downward motion. The weight is causing it to accelerate, and the drag force is causing it to decelerate.
Net downward force = Weight + Drag force = mass * acceleration
The weight is constant, but the drag force increases as the downward velocity increases. When the drag force is equal to the weight, the net downward force is 0 N. And the acceleration is 0 m/s^2. This means the velocity will not increase. The terminal velocity is the velocity at the time when the drag force is equal to the weight.
Fd = -b * v, Weight = m * g
-b * v = m * g,
-b * 5 = 4 *10^−5 * 9.8
-b = (4 *10^−5 * 9.8) ÷ 5= -7.84 * 10^-5
b = 7.84 * 10^-5
B) Assuming a drag force determine the time required for such a drop, starting from rest, to reach 63% of terminal velocity
Time = (vf – vi) ÷ a, vf = 63% of terminal velocity, vi = 0 m/s
Time = 63% of terminal velocity ÷ a
Weight + Drag force = mass * acceleration
Weight = 3.92* 10^-4 N
Drag force = -7.84 * 10^-5 * v
63% of terminal velocity = 0.63 * 5 = 3.15 m/s = vf
Drag force = -7.84 * 10^-5 * 3.15 = -2.4696 * 10^-4 N
(3.92* 10^-4) + (-2.4696 * 10^-4) = 4 * 10^-5 * acceleration
Acceleration = (3.92 * 10^-4 – 2.4696 * 10^-4) ÷ (4 * 10^-5) = 3.626 m/s^2
Time = (3.15 ÷ 3.626) seconds
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A) Assuming a drag force determine the value of the constant b
force on the raindrop F=mg
mg = -bv
b=- mg/v
Assuming a drag force determine the time required for such a drop, starting from rest, to reach 63% of terminal velocity.
Need solution to differential equation to give you an equation of velocity as a function of time
m(dv/dt) - bv =0
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The arrow keys ought to administration course - that's the organic and organic inclination. Use J for leaping, F to increasw stress, shift F or ctrl-F to cut back it, A for acceleration, V for velocity (assuming which you at the instant are not portraying rather physics - indoors the rather international, increasing stress creates acceleration that will boost velocity).