A 0.5 kg block moving at a speed of 12 ms -1 compresses a spring through a distance 30 cm when its speed is halved. The spring constant of the spring will be Nm -1.

Question

A 0.5 kg block moving at a speed of 12 ms -1 compresses a spring through a distance 30 cm when its speed is halved. The spring constant of the spring will be Nm -1. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

U i + K i = U f + K f ⇒ 0+(1/2) m (12)2=(1/2) K (0.3)2+(1/2) m (6)2 ⇒ 0.5(122-62)= K (0.3)2 K =600 N / m

Q. A $0.5 k g$ block moving at a speed of $12 m s^{- 1}$ compresses a spring through a distance $30 c m$ when its speed is halved. The spring constant of the spring will be ______ $N m^{- 1}$ .

$U_{i} + K_{i} = U_{f} + K_{f}$
$\Rightarrow 0 + \frac{1}{2} m (12)^{2} = \frac{1}{2} K (0.3)^{2} + \frac{1}{2} m (6)^{2}$
$\Rightarrow 0.5 (1 2^{2} - 6^{2}) = K (0.3)^{2}$
$K = 600 N / m$

Q. A 0.5kg block moving at a speed of 12ms−1 compresses a spring through a distance 30cm when its speed is halved. The spring constant of the spring will be ______ Nm−1.

Ui​+Ki​=Uf​+Kf​ ⇒0+21​m(12)2=21​K(0.3)2+21​m(6)2 ⇒0.5(122−62)=K(0.3)2 K=600N/m

Q. A $0.5 k g$ block moving at a speed of $12 m s^{- 1}$ compresses a spring through a distance $30 c m$ when its speed is halved. The spring constant of the spring will be ______ $N m^{- 1}$ .

$U_{i} + K_{i} = U_{f} + K_{f}$
$\Rightarrow 0 + \frac{1}{2} m (12)^{2} = \frac{1}{2} K (0.3)^{2} + \frac{1}{2} m (6)^{2}$
$\Rightarrow 0.5 (1 2^{2} - 6^{2}) = K (0.3)^{2}$
$K = 600 N / m$