Question

A T-shirt cannon is made of pipe within which a light spring, with k=100 N/m, can be compressed to launch the bundled shirt of mass 0.3 kg. Imagine the spring compressed 0.15 m and then released. Ignoring friction, calculate the launch velocity (speed at which the T-shirt leaves the spring) in two cases: A horizontal launch A vertical launch HTML EditorKeyboard Shortcuts

Answer 1

Horizontal launch

`\vec v = 2.739\cdot i \,\left[(m)/(s) \right]`

Vertical launch

`\vec v = 2.739\cdot j \,\left[(m)/(s) \right]`

Step-by-step explanation:

The launch speed is calculated by means of the Principle of Energy Conservation:

`U_(k) = K`

`(1)/(2)\cdot k \cdot x^(2) = (1)/(2)\cdot m \cdot v^(2)`

`v = x \cdot \sqrt{(k)/(m) }`

`v = (0.15\,m)\cdot \sqrt{(100\,(N)/(m) )/(0.3\,kg) }`

`v \approx 2.739\,(m)/(s)`

The velocities for each scenario are presented herein:

Horizontal launch

`\vec v = 2.739\cdot i \,\left[(m)/(s) \right]`

Vertical launch

`\vec v = 2.739\cdot j \,\left[(m)/(s) \right]`