Question

What is the force constant of a spring which is stretched
a 2 mm by a force of 4 N,
b 4 cm by a mass of 200 g?

Answer 1

To find:

Force constant of a spring in the following cases:

• 2 mm by a force of 4 N

• 4 cm by a mass of 200 g

Calculation:

We will consider that at the given extension , the spring force is equal and opposite to the applied force.

In the 1st case:

$\rm\therefore \: force = - kx$

$\rm = > \: - 4= - k(2 \times {10}^{ - 3} )$

$\rm = > \: 4= k(2 \times {10}^{ - 3} )$

$\boxed{ \rm = > \: k = 2000 \: N {m}^{ - 1} }$

In the 2nd case:

$\rm\therefore \: force = - kx$

$\rm = > \: - \dfrac{200}{1000} \times g = - k(4 \times {10}^{ - 2} )$

$\rm = > \: \dfrac{200}{1000} \times 10 = k(4 \times {10}^{ - 2} )$

$\rm = > \: \dfrac{2000}{1000} = k(4 \times {10}^{ - 2} )$

$\rm = > \: 2 = k(4 \times {10}^{ - 2} )$

$\rm = > \: k = 0.5 \times {10}^{2}$

$\boxed{ \rm = > \: k =50 \: N {m}^{ - 1} }$

Hope It Helps.