How far x does it move down the incline before coming to rest? Suppose the incline is frictionless. The angle of inclination is 36 ◦ , the spring constant is 89.6 N/m the mass of the block is 9.05 kg and the acceleration of gravity is 9.8 m/s2 .

Question

How far x does it move down the incline before coming to rest? Suppose the incline is frictionless. The angle of inclination is 36 ◦ , the spring constant is 89.6 N/m the mass of the block is 9.05 kg and the acceleration of gravity is 9.8 m/s2 .
Answer in units of m
Choosing down the incline as the positive direction, what is its acceleration at its lowest point?
Answer in units of m/s2

sly · Answer

weight component down incline = m g sin 36
= 9.05 * 9.8* sin 36
= 52.1 Newtons compressing spring
work done by gravity = energy in spring
52.1 x = (1/2) 89.6 x^2
x = 1.16 m
F spring = 89.6 * 1.16 =104 Newtons up incline
net force up = 104 - 52.1 = 52.1 up
a = F/m = 52.1/9.05 = 5.76 m/s^2