You have a light spring which obeys Hooke's law. This spring stretches 2.66 cm vertically when a 2.70 kg object is suspended from it. Determine the following. (a) the force constant of the spring (in N/m).

(b) the distance (in cm) the spring stretches if you replace the 2.70 kg object with a 1.35 kg object.

(c) the amount of work (in J) an external agent must do to stretch the spring 8.40 cm from its unstretched position.

a) k = 994.74 N/m

b) Δx = 0.0133 m

c) W = 7.02 J

Explanation:

a) let Δd = 2.66*10^-2 m and the forces acting on the object at 2.66 cm are the force by spring Fs and force by gravity Fg such that:

Fs = Fg

k*Δd = m*g

k = (m*g) / (Δd)

k = (2.70*9.8) / (2.66*10^-2)

k = 994.74 N/m

b) let Δx be the distance the spring stretches and the forces acting on the object at Δx are the force by spring Fs and force by gravity Fg such that:

Fs = Fg

k*Δx = m*g

Δx = (m*g) / (k)

= (1.35*9.8) / (994.74)

= 0.0133 m

c) when the spring stretch X = 8.40 cm the only forces are Fs = force by spring and F = force by external agent such that:

F = Fs

= k*X

= (994.74) * (8.40*10^-2)

= 83.56 N

then the work done by the external agent is given by:

W = F*X

= (83.56) * (8.40*10^-2)

= 7.02 J