Question

A spring stores 5 J of energy when stretched by 25 cm. It is kept vertical with the lower end fixed. A block fastened to its other end is made to undergo small oscillations. If the block makes 5 oscillations each second, what is the mass of the block?

Answer 1

Total Energy = 5 J.

x = 25 cm. = 0.25 m.

Using the formula,

E = 1/2 kx²

∴ 5 × 2 = k × 625/10⁴

k =  10⁵/625

k = 160 N/m.

Now, frequency = 5

∴ T = 0.2 seconds. (T = 1/Frequency).

Using the formula,

T = 2π√(m/k)

0.2 = 2π√(m/160)

∴ m = 0.16 kg.

Hence, the mass is 0.16 kg. or 160 g.

Hope it helps.

Answer 2

$<b>$Sol. .

x = 25cm = 0.25m

E = 5J

f = 5

So,

T = 1/5sec.

Now

P.E. = (1/2) kx2

⇒(1/2) kx2 = 5

⇒ (1/2) k (0.25)2 = 5

⇒ k = 160 N/m.

Again, T = 2π √(m/k)

⇒ 1/5 = 2π √(m/160)

⇒ m = 0.16 kg.