A stone of mass 20g is released from a catapult whose rubber is stretched through 5cm. If the force constant of the rubber is 200Nm\(^{-1}\), calculate the ...
Question 1 Report
A stone of mass 20g is released from a catapult whose rubber is stretched through 5cm. If the force constant of the rubber is 200Nm\(^{-1}\), calculate the speed with which the stone leaves the catapult.
Answer Details
The stretched rubber stores elastic potential energy, which is converted into the kinetic energy of the stone when it is released.
Data: mass \(m = 20\ \text{g} = 0.02\ \text{kg}\); extension \(x = 5\ \text{cm} = 0.05\ \text{m}\); force constant \(k = 200\ \text{Nm}^{-1}\).
Elastic potential energy stored in the rubber:
\[ E = \tfrac{1}{2}kx^{2} = \tfrac{1}{2}\times200\times(0.05)^{2} = \tfrac{1}{2}\times200\times0.0025 = 0.25\ \text{J} \]By conservation of energy, this equals the kinetic energy of the stone as it leaves the catapult:
\[ \tfrac{1}{2}mv^{2} = 0.25 \] \[ v^{2} = \frac{2\times0.25}{0.02} = \frac{0.5}{0.02} = 25 \] \[ v = \sqrt{25} = 5\ \text{ms}^{-1} \]The stone leaves the catapult with a speed of \(5\ \text{ms}^{-1}\).
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