Question

A block with mass m1 = 9.1 kg is on an incline with an angle θ = 31° with respect to the horizontal. For the first question there is no friction, but for the rest of this problem the coefficients of friction are: μk = 0.3 and μs = 0.33.

1) To keep the mass from accelerating, a spring is attached. What is the minimum spring constant of the spring to keep the block from sliding if it extends x = 0.14 m from its unstretched length.

2) Now a new block with mass m₂ = 14.7 kg is attached to the first block. The new block is made of a different material and has a greater coefficient of static friction. What minimum value for the coefficient of static friction is needed between the new block and the plane to keep the system from accelerating?

Note: I got help earlier today on this problem, but when I worked through it, the answer wasn't correct 1) Came out to 349 n/m and 2) Came out to 0.6. I really could use some help here.

Also

Scientists want to place a 3700 kg satellite in orbit around Mars. They plan to have the satellite orbit a distance equal to 1.9 times the radius of Mars above the surface of the planet. Here is some information that will help solve this problem:

m_mars = 6.4191 x 10²³ kg
r_mars = 3.397 x 10⁶ m
G = 6.67428 x 10^-11 N-m²/kg²

What should the radius of the orbit be (measured from the center of Mars), if we want the satellite to take 8 times longer to complete one full revolution of its orbit?

We haven't learned Kepler's 3rd Law, any help would be appreciated.

Answer 1

1) If the spring constant is k, we have, kx mag (sin θ-u, cos θ) k= 9.1x9.8 xl sin(31)-0.33xcos(31)」 k-147.89 N/m Therefore, the minimum spring constant is k-147.89 N/m 2) Now, putting a-0 0.14 m,g(sin θ-u: cos θ)=0 =tan θ 4 tan (31) A, =0.6 Therefore, the minimum coeffici ent of static friction is u0.6