A block of mass 11.2 kg slides from rest down a frictionless 24.0° incline and is stopped by a strong spring with a spring constant 31.3 kN/m (note the unit). The block slides 8.90 m from the point of release to the point where it comes to rest against the spring. When the block comes to rest momentarily, how far has the spring been compressed? Answer in units of cm and use 9.8 m/s2 for g.

Question

A block of mass 11.2 kg slides from rest down a frictionless 24.0° incline and is stopped by a strong spring with a spring constant 31.3 kN/m (note the unit). The block slides 8.90 m from the point of release to the point where it comes to rest against the spring. When the block comes to rest momentarily, how far has the spring been compressed? Answer in units of cm and use 9.8 m/s2 for g.
I can't really figure out how to start to try to solve this problem. Help please?

Henry · Answer

Fb = m*g = 11.2kg * 9.8N/kg = 109.8 N. = Force of block. Fp = 109.8*sin24 = 44.64 N. = Force parallel to the incline. d = (1m/31,300N) * Fp d = (1m/31,300N) * 44.64N = 0.0014262 m. = 0.143 cm.