A 1.60 kg object is held 1.10 m above a relaxed, massless vertical spring with a force constant of 330 N/m. The object is dropped onto the spring. (a) How far does the object compress the spring? m (b) Repeat part (a), but now assume that a constant air-resistance force of 0.650 N acts on the object during its motion. m (c) How far does the object compress the spring if the same experiment is performed on the moon, where g = 1.63 m/s2 and air resistance is neglected? m
here,
mass , m = 1.6 kg
height , h = 1.1 m
force constant , K = 330 N/m
a)
let the spring compresses x m
using conservation of energy
0.5 * k * x^2 = m * g* ( h + x)
0.5 * 330 * x^2 = 1.6 * 9.81 * ( 1.1 + x)
solving for x
x = 0.37 m
b)
resistive force , F = 0.65 N
work done by F = initial potential energy - final energy stored in spring
F * (h + x) = m * g * (h + x) - 0.5 * k * x^2
0.65 * (1.1 + x) = 1.6 * 9.81 * ( 1.1 + x) - 0.5 * 330 * x^2
solving for x
x = 0.365 m
c)
on moon , g = 1.63 m/s^2
let the spring compresses x m
using conservation of energy
0.5 * k * x^2 = m * g* ( h + x)
0.5 * 330 * x^2 = 1.6 * 1.63 * ( 1.1 + x)
solving for x
x = 0.14 m
Get Answers For Free
Most questions answered within 1 hours.