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A spring has an unstretched length of 10 cm. It exerts a restoring force F when stretched to a length of 11 cm.
a. For what length of the spring is its restoring force 3F?
b. At what compressed length is the restoring force 2F
a) The length for 3F force is : 13 cm
b) The length for 2F force is : 8 cm


Sagot :

The required length and compressed length of the spring at the given force values are 13 cm and 8 cm respectively.

Explanation:

F = ke

k = spring constant ;

e = extension;

e = (Final length - Initial length)

Initial length, l = 10

Final length = L1 = 11

F = k(11 - 10)

F = k;

Length for a restoring force of 3F ;

3F = k(Final length - Initial length)

k = F

3F = F(L1 - 10)

3F = - 10F + F(L1)

F(L1) = 3F + 10F

F(L1) = 13F

L1 = 13

Hence, required length ls 13 cm

B.)

Let compressed length = c

2F = F(initial length - compressed length)

2F = F(10 - c)

2F = 10F - F(c)

F(c) = 10F - 2F

F(c) = 8F

c = 8F / F

c = 8 cm

Therefore, the required compressed length ls 8 cm

Spring:

A spring is an elastic body that stores mechanical energy. Coil springs are often used in daily life, but there are many different types of springs. Modern quills are usually made of spring steel, but non-metallic items like bows are also quills.

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