Question

Students are collecting data as they control the toy helicopter shown. The helicopter has a mass m and must exert a thrust of power P0 to initially move upward with a constant speed v0 . The students then cause the helicopter to exert a thrust so that a net force Fnet=2mg accelerates it upward. As the helicopter is accelerating, it has a thruster power Pf , and as it passes a height h0 it has a speed of 3v0. The ratio PfP0 is most nearly
0.11

Answer A: 0.11
Answer B: 0.17
Answer C: 4
Answer D: 6
Answer E: 9

Answer 1

The ratio of the final thrust to initial thrust of the helicopter is 6.

The given parameters;

• mass of the helicopter, = m
• thrust power, = Po
• initial speed of the helicopter = Vo
• net force = 2mg
• final thrust power = Pf
• speed at height (h) = 3vo

The thrust power of the helicopter is calculated as follows;

P = Fv

where;

• F is the net force on the helicopter
• v is the speed of the helicopter
• P is the thrust power

The initial thrust power of helicopter is calculated as follows;

P₀ = Fv₀

The final thrust power of the helicopter is calculated as follows;

Pf = F(3v₀) = 2mg(3v₀)

The ratio of the final thrust to initial thrust of the helicopter is calculated as follows;

$\frac{P_f}{P_o} = \frac{(2mg)(3v_0)}{Fv_0} = \frac{(2mg)(3v_0)}{(mg)v_0} = 6$

Thus, the ratio of the final thrust to initial thrust of the helicopter is 6.

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