Question

I have three different homework questions I cannot seem to get
My hw is due at 12 so if anyone can help that would be helpful

Thank you

1)   For a car moving with speed v, the force of air drag is proportional to v². If the power output of the car's engine is quadrupled, by what factor does the speed of the car increase?

2)Tarzan

(m = 76 kg)

commutes to work swinging from vine to vine. He leaves the platform of his tree house and swings on the end of a vine of length

L = 8.0 m.

(a) If the platform is 1.5 m above the lowest point in the swing, what is the tension in the vine at the lowest point in the swing?
kN

(b) Tarzan again takes to his morning commute, but this time a monkey of mass

m_M = 30 kg

hitches a ride by jumping onto Tarzan's back. If a vine can withstand a maximum tension of 1200 N, will it snap under the tension of the added passenger?

Yes No

If so, at what angle with respect to the vertical does the vine break? (If the vine does not break, enter NONE.)

3) A wheel of mass 13 kg is pulled up a step by a horizontal rope as depicted in the figure below. If the height of the step is equal to one-fifth the radius of the wheel,

h = 1/5 R

what minimum tension is needed on the rope to start the wheel moving up the step? Hint: The wheel will start to move just as the normal force on the very bottom of the wheel becomes zero.

Answer 1

1)

Power absorbed by air drag = v^3 * Cd
Say 30 m/s , Cd = 0.45
Power absorbed = 12,150 Watts
Double the power = 24,300 Watts
24,300 = v^3 * 0.45
v = cube root ( 24,300 / 0.45 )
v = 37.7976 m/s
increased by 25.99%

2)

Tarzan (m= 74kg) commutes to work swinging from vine to vine. He leaves the platform of his tree house and swings on the end of a vine of length L=8.0m.
(a) If the platform is 1.9m above the lowest point in the swing, what is the tension in the vine at the lowest point in the swing?
(b) Tarzan again takes to his morning commute, but this time a monkey of mass m subscript m=23kg hitches a ride by jumping onto Tarzan's back. If a vine can withstand a maximum tension of 1200 N, will it snap under the tension of the added pasenger? If so, at what angle with respect to the vertical does the vine break?

Using v^2 = 2 gh
At the lowest point
v^2 = 2*9.8 * 1.9 = 37.24 (m/s)^2
Tension T = m v^2/ L + mg = {74 * 37.24 / 8} + 74*9.8 = 1069.67N = 1.1 KN
----
-In the second case it will break.
When the string makes an angle ?, h = 1.9