A fairground sling-shot is shown below - Leaving Cert Physics - Question 6 - 2017

The pod has kinetic energy due to its motion. Kinetic energy can be calculated using the formula:

$KE = \frac{1}{2} mv^2$
where $m$ is the mass of the pod and $v$ is its velocity.

At its highest point, the pod possesses potential energy. This energy is due to its position in a gravitational field and can be calculated using:

$PE = mgh$
where $m$ is the mass of the pod, $g$ is the acceleration due to gravity, and $h$ is the height.

The occupants experience apparent weightlessness because at the pod’s highest point, they are in free fall. At this point, the force of gravity acting on them is unopposed, causing them to feel weightless.

The potential energy stored in the springs is given by:

$PE = mgh$

Given:

• Mass, $m = 400 ext{ kg}$
• Gravitational acceleration, $g = 9.8 ext{ m/s}^2$
• Height, $h = 50 ext{ m}$

Therefore,

$PE = 400 imes 9.8 imes 50 = 196000 ext{ J}$

The forces acting on the pod when it is released can be illustrated as follows:

• Weight (W) acting downwards due to gravity: ( W = mg )
• Spring Force (F_s) acting upwards, exerted by the springs.

In a diagram, represent the pod with an arrow pointing down labeled as 'Weight' and an arrow pointing up labeled as 'Spring Force'.

To find the maximum height, use the principle of conservation of energy where the kinetic energy will convert to potential energy at the highest point.

Maximum Height:

$KE = PE$

$\frac{1}{2} mv^2 = mgh$

Rearranging gives:

$h = \frac{\frac{1}{2} mv^2}{mg} = \frac{v^2}{2g}$

Substituting values:

$h = \frac{(8)^2}{2 imes 9.8} \approx 3.27 ext{ m}$

One energy loss that might prevent the pod from reaching its maximum height is air resistance.