Answer:
(A) l = 0.39 m
(B) l =0.38 m
(C) l = 0.14 m
Explanation:
Answer:
Explanation:
Answer:
Explanation:
from the question we are given the following values:
mass (m) = 1.6 kg
height (h) = 1.05 m
compression of spring (l) = ?
spring constant (k) = 330 N/m
acceleration due to gravity (g) = 9.8 m/s^{2}
(A) initial potential energy of the object = final potential energy of the spring
potential energy of the object = mg(1.05 + l)
potential energy of the spring = 0.5 x k x l^{2} (k= spring constant)
therefore we now have
mg(1.05 + l) = 0.5 x k x l^{2}
1.6 x 9.8 x (1.05 + l) = 0.5 x 300 x l^{2}
15.68 (1.05 + l) = 150 x l^{2}
16.5 + 15.68l = 150l^{2}
l = 0.39 m
(B) with constant air resistance the equation applied in part A above becomes
initial P.E of the object - air resistance = final P.E of the spring
mg(1.05 + l) - 0.750(1.05 + l) = 0.5 x k x l^{2}
1.6 x 9.8 x (1.05 + l) - 0.750(1.05 + l) = 0.5 x 300 x l^{2}
(16.5 + 15.68l) - (0.788 + 0.75l) = 150l^{2}
16.5 + 15.68l - 0.788 - 0.75l = 150l^{2}
15.71 + 14.93l = 150^{2}
l =0.38 m
(C) where g = 1.63 m/s^{2} and neglecting air resistance
the equation mg(1.05 + l) = 0.5 x k x l^{2} now becomes
1.6 x 1.63 x (1.05 + l) = 0.5 x 300 x l^{2}
2.608 (1.05 +l) = 0.5 x 300 x l^{2}
2.74 + 2.608l = 150 x l^{2}
l = 0.14 m
