A 1.0 kg mass is pressed against a spring, compressing it 0.30 m as shown. The m
ID: 1466685 • Letter: A
Question
A 1.0 kg mass is pressed against a spring, compressing it 0.30 m as shown. The mass is released from rest and the spring launches it up the hill-when the spring gets to the relaxed position the 1.0 kg mass leaves the spring behind and climbs the hill. (The mass is not attached to the spring.)The spring constant is 50 N/m. Determine the maximum vertical height y above its initial position that the mass rises if there is no friction. Suppose there HAD been friction and the mass only rose 0.15 m above its initial position-what would the kinetic friction coefficient have been?Explanation / Answer
if there is no friction
then
use law of conservation of energy
0.5*k*x^2 = work done by gravitational force = m*g*S
S is the distance travelled along the inclined plane
0.5*50*0.3*0.3 = 1*9.81*S
S = 0.23 m
total distance from the initial position is 0.3+0.23 = 0.53 m
maximum vertical height is hmax = 0.53*sin(30) = 0.265 m
B) Work done by the friction = E2-E1 = (m*g*hmax) - (0.5*k*x^2) = (1*9.81*0.15)-(0.5*50*0.3*0.3) =-0.7785 J
-mu*m*g*cos(30) = -0.7785
mu = 0.7785/(1*9.81*cos(30)) = 0.0916
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