This Assignment is due within two hours and I cannot find any solution for these

Question

This Assignment is due within two hours and I cannot find any solution for these two questions. I have tried working them out but to no avail, I cannot find a solution. So Please help me out and direct me to a solution please!!! Thanks.

1) Suppose that due to a gravitational torque exerted by the Moon on the Earth, our planet's rotation slows at a rate of 2.20 ms/century.

(a) Calculate the Earth's angular acceleration due to this effect.
_______ rad/s2
(b) Calculate the torque exerted by the Moon on the Earth.
________ N·m
(c) Calculate the length of the wrench an ordinary person would need to exert such a torque, as in Figure P10.67. Assume the person can brace his feet against a solid firmament and exert a 800 N force.
_________ m



The Second Problem

2) Four people, each with a mass of 72.9 kg, are in a car with a mass of 1150 kg. An earthquake strikes. The driver manages to pull of the road and stop, as the vertical oscillations of the ground surface make the car bounce up and down on its suspension springs. When the frequency of the shaking is 1.90 Hz, the car exhibits a maximum amplitude of vibration. The earthquake ends and the four people leave the car as fast as they can. By what distance does the car's undamaged suspension lift the car's body as the people get out?
_______________cm



Thank you so much, any help will be very appreciated. :)

Explanation / Answer

1) Suppose that due to a gravitational torque exerted by the Moon on the Earth, our planet's rotation slows at a rate of 2.20 ms/century. (a) Calculate the Earth's angular acceleration due to this effect. w=2pi/T so dw=-dT2pi/T^2. so dw/dt=-dT*2pi/dt*T^2 where dT/dt=2.2e-3/100*365*86400. dw/dt=5.87e-22(rad/s2). (b) Calculate the torque exerted by the Moon on the Earth. 5.87e-22*6e24*2*6400e3^2/5=5.7e16(Nm) (c) Calculate the length of the wrench an ordinary person would need to exert such a torque, as in Figure P10.67. Assume the person can brace his feet against a solid firmament and exert a 800 N force. L=5.7e16/800=7.2e13(m) The Second Problem 2) Four people, each with a mass of 72.9 kg, are in a car with a mass of 1150 kg. An earthquake strikes. The driver manages to pull of the road and stop, as the vertical oscillations of the ground surface make the car bounce up and down on its suspension springs. When the frequency of the shaking is 1.90 Hz, the car exhibits a maximum amplitude of vibration. The earthquake ends and the four people leave the car as fast as they can. By what distance does the car's undamaged suspension lift the car's body as the people get out? ---- the natural frequency must be 1.9Hz. so 1.9*2pi=sqrt(k/m)=sqrt(k/(1150+72.9*4)) so k = 2.1e5(N/m). ---- the distance to equilibrium. (Amplitude of SHM when the 4 people get out) 4*72.9*g/k=0.0136(m). so that maximum distance 2*0.0136=0.0272(m)

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