You are asked to design a spring that will give a 1160-kg satellite a speed of 2.50 m/s relative to an orbiting space shuttle. Your spring is to give the satellite a maximum acceleration of 5.00 g. The spring’s mass, the recoil kinetic energy of the shuttle, and changes in gravitational potential energy will all be negligible. (a) What must the force constant of the spring be? (b) What distance must the spring be compressed?
Solution 25E Step 1: Kinetic energy of satellite=energy from the spring. 1/2 mv = 1/2kx 1 Where m mass of satellite(m = 1660 kg). velocity of satellite(v = 2.85 m/s). k spring constant x length at which spring needs to be compressed. Step 2: (a). Substitutes all known values in eq 1 2 1/2 (1160 kg)(2.85 m/s) = 1/2kx 2 kx = 9422.1 2 Using newton’s second law of motion F = ma kx = ma Where a acceleration of the satellite Substituting the values kx = (1160 kg)(5 *.8) kx = 56840 Solving for x x = 56840/k 3 Substituting eq 2 in eq 3 k(56840/k) = 9422.1 Simplifying above equation becomes (56840) /k = 9422.1 k = (56840) /9422.1 k = 342894 N/m