Answer:
Answer:
a. 1.594 m/s = v
b. 1.274 m/s = v
Explanation:
A) First calculate the potential energy stored in the spring when it is compressed by 0.180 m...
U = 1/2 kx²
Where U is potential energy (in joules), k is the spring constant (in newtons per meter) and x is the compression (in meters)
U = 1/2(13.0 N/m)(0.180 m)² = 0.2106 J
So when the spring passes through the rest position, all of its potential energy will have been converted into kinetic energy. K = 1/2 mv².
0.2106 J = 1/2(0.170 kg kg)v²
0.2106 J = (0.0850 kg)v²
2.808m²/s² = v²
1.594 m/s = v
(B) When the spring is 0.250 m from its starting point, it is 0.250 m - 0.180 m = 0.070 m past the equilibrium point. The spring has begun to remove kinetic energy from the glider and convert it back into potential. The potential energy stored in the spring is:
U = 1/2 kx² = 1/2(13.0 N/m)(0.070 m)² = 0.031J
Which means the glider now has only 0.2106 J - 0.031J = 0.1796 J of kinetic energy remaining.
K = 1/2 mv²
0.1796 J = 1/2(0.170 kg)v²
0.138 J = (0.0850 kg)v²
1.623 m²/s² = v²
1.274 m/s = v
