3. (a) What is the magnitude of the force of gravity (the weight) of a strand of

Question

3. (a) What is the magnitude of the force of gravity (the weight) of a strand of human hair which has a mass of 40.3 milligrams? Give your answer in newtons (N) to 2 significant figures.

(b) An aircraft has an initial mass of m0 and an initial acceleration of a0. After flying for 2 hours, the mass of the aircraft has decreased by 11%, due to the burning of the fuel. If the propulsive force provided by the engines is constant, what is the expression for the new acceleration, a2, at this time? You may assume that the aircraft is in level flight at all times and the air resistance is negligible. Select one: (a) a2=a0/0.89 (b) a2=0.89a0 (c) a2=1.11a0 (d) a2=1+0.11a0

(c) An Angry Bird sits on a clothes line midway between the two poles (see diagram).

If the combined weight of the bird and rope is W, what is the tension in the rope in terms of and W?

Select one: (a) W tan (b) W/(2sin) (c) W/(2cos) (d) W cos / sin

Explanation / Answer

a)

W = mg

where

g = 9.8 m/s^2

m = 40.3 mg = 4.03 x 10^-5 kg

W = 4.03 X 10^-5 X 9.8

W = 3.95 X 10^-4 N

b)

F = ma = constant

moao = m2a2

a2 = moao / m2

m2 = 0.89mo

a2 = aomo / 0.89mo

a2 = ao / 0.89

c)

From Newton's 2nd law, the net vertical forces are:

F = 0 = Tsin + Tsin - w

Where the tension T occurs twice because the line is effectively split into two pieces, and w is the weight. Therefore:

0 = Tsin + Tsin - w
2Tsin = w
T = w / 2sin

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