A helicopter descends vertically to land with a speed of 4.0 m/s.If the shock absorbers have an initial length of 0.50 m,they compress to 79% of their original length and the air in the tires absorbs 21% of the initial energy as heat,what is the ratio of the spring constant to the helicopter's mass? Assume one landing gear in the craft.
A)1.1 kN/kg-m
B)1.1 N/kg-m
C)11 N/kg-m
D)0.11 kN/kg-m

Question

Quizplus · Accepted Answer

The energy absorbed by the shock absorbers is:$$E_s = \frac{1}{2}kx_0^2(1-0.79^2) = 0.36kx_0^2$$The energy absorbed by the air in the tires is:$$E_t = 0.21E_i = 0.21(mgh)$$The total energy absorbed is:$$E_a = E_s + E_t = 0.36kx_0^2 + 0.21mgh$$The work done by gravity is:$$W_g = mgh$$The ratio of the spring constant to the helicopter's mass is:$$\frac{k}{m} = \frac{E_a}{W_g} = \frac{0.36kx_0^2 + 0.21mgh}{mgh} = 0.36\frac{x_0^2}{h} + 0.21$$Substituting the given values, we get:$$\frac{k}{m} = 0.36\frac{(0.50 	ext{ m})^2}{4.0 	ext{ m}} + 0.21 = 1.1 	ext{ kN/kg-m}$$

A Helicopter Descends Vertically to Land with a Speed of 4.0