Use the worked example above to help you solve this problem. A 0.390 kg object a

Question

Use the worked example above to help you solve this problem. A 0.390 kg object attached to a spring of force constant 1.10 times 10^2 N/m is free to move on a frictionless horizontal surface. If the object is released from rest at x = 0.100 m, find the force on it and its acceleration at x = 0.100 m, x = 0.0500 m, x = 0 m, x = 0.0500 m, and x = -0.100 m Use the values from the PRACTICE IT section. For the same spring and mass system, find the force exerted by the spring and the position x when the object's acceleration is +8.55 m/s^2.

Explanation / Answer

(a)

We know that,

F = -k*x

if x = 0.100 m,

F = 1.1*10^2 * 0.10 = 11 N

a = F / m = 28.2 m/s^2

if x = 0.050 m,

F = 1.1*10^2 * 0.050 = 5.5 N

a = 14.1 m/s^2

if x = 0 , F = 0

if x = -0.050 m,

F = -5.5 N

a = -14.1 m/s^2

if x = -0.100 m,

F = -11 N

a = -28.2 m/s^2

(b)

if a = 8.55 m/s^2

F = m*a = 3.33 N

x = F / k = 3.33 / 110

x = 0.0303 m = 3.03 cm

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