You have a light spring which obeys Hooke's law. This spring stretches 3.08 cm vertically when a 2.20 kg object is suspended from it. Determine the following. (a) the force constant of the spring (in N/m) N/m (b) the distance (in cm) the spring stretches if you replace the 2.20 kg object with a 1.10 kg object cm (c) the amount of work (in J) an external agent must do to stretch the spring 7.00 cm from its unstretched position
You have a light spring which obeys Hooke's law. This spring stretches 3.08 cm vertically when a 2.20 kg object is suspended from it. Determine the following. (a) the force constant of the spring (in N/m) N/m (b) the distance (in cm) the spring stretches if you replace the 2.20 kg object with a 1.10 kg object cm (c) the amount of work (in J) an external agent must do to stretch the spring 7.00 cm from its unstretched position
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Transcribed Image Text:You have a light spring which obeys Hooke's law. This spring stretches 3.08 cm vertically when a 2.20 kg object is suspended from it. Determine the following.
(a) the force constant of the spring (in N/m)
N/m
(b) the distance (in cm) the spring stretches if you replace the 2.20 kg object with a 1.10 kg object
cm
(c) the amount of work (in J) an external agent must do to stretch the spring 7.00 cm from its unstretched position
Expert Solution

Step 1
Subpart (a):
When the spring is stretched by the object, the weight of the object provides the necessary force to stretch the spring vertically.
The formula to calculate the weight of the object is given by
Here, is the weight, is the mass of the object and is the acceleration due to gravity.
If we apply Hook's law to the spring, we can write,
Here, is the force constant and is the vertical displacement of the spring due to the load. Here, only the magnitude of the force is considered.
Equate equation (1) and equation (2) and simplify to obtain the force constant of the spring.
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