Answer:
a) the distance up to which the object compress the spring is x = 0.378m
b),the distance up to which the object compress the spring is x= 0.359
Explanation:
Given that,
Mass , m = 1.6kg
spring at vertical height ,h = 1.05m
Spring constant ,k = 315 N/m
Air resistance force = 0.750N
Let assume that the lowest point is the origin
Therefore, initial displacement is
And final displacement is
Apply the conservation of energy
solve the equation using quadratic equation
Take the positive value
Hence , the distance up to which the object compress the spring is x = 0.378m
b)If the air resistance is taken into cosideration
therefore apply conservation of energy
mg(1.05 + x) - fd = kx²/2
mg(1.05 +x) - (0.750N) (1.05 + x) = kx²/2
((1.60× 9.81) - 0.750)(1.05 + x) = (315/2)x²
14.946 (1.05 + x) = 157.5x²
15.6933 + 14.946x = 157.5x²
x² - 0.0949x - 0.00996
solve the equation using quadratic equation
x = 0.359 or -0.264
Hence ,the distance up to which the object compress the spring is x= 0.359