Some kids playing at the park get creative, and they turn a seesaw into a trebuchet – they slide the plank until only 20 cm of its total length of 4 m extends from one side of the fulcrum. While bracing the system in a horizontal position, they place a 0.5 kg cantaloupe on the really long end, and three 25 kg kids sit on the short end (assume at the very end). Once the braces are removed, the kids fall, flinging the cantaloupe. What maximum velocity does the cantaloupe reach? Ignore the mass of the plank.

Question

Some kids playing at the park get creative, and they turn a seesaw into a trebuchet – they slide the plank until only 20 cm of its total length of 4 m extends from one side of the fulcrum. While bracing the system in a horizontal position, they place a 0.5 kg cantaloupe on the really long end, and three 25 kg kids sit on the short end (assume at the very end). Once the braces are removed, the kids fall, flinging the cantaloupe. What maximum velocity does the cantaloupe reach? Ignore the mass of the plank.

Answer 1

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Answer 2

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Answer 3

To find the maximum velocity reached by the cantaloupe, we can apply the principle of conservation of energy. The potential energy of the system (cantaloupe and kids) is transformed into kinetic energy as it is flung from the trebuchet.

First, let's calculate the potential energy of the system before releasing the cantaloupe. The potential energy is given by:

Potential Energy (PE) = mass × acceleration due to gravity × height

The height in this case is the distance from the fulcrum to the point where the cantaloupe is placed.

Height = (Total length of the plank - length extended from fulcrum) = 4 m - 20 cm = 3.8 m

So, the potential energy is:

PE = (0.5 kg + 3 * 25 kg) × 9.8 m/s^2 × 3.8m

Next, we can calculate the kinetic energy of the cantaloupe when it reaches its maximum velocity. The kinetic energy is given by:

Kinetic Energy (KE) = 0.5 × mass × velocity^2

In this case, we do not have the velocity yet, so we can express it in terms of the potential energy:

PE = KE

(0.5 kg + 3 * 25 kg) × 9.8 m/s^2 × 3.8m = 0.5 × 0.5 kg × velocity^2

Now we can solve for the velocity:

velocity^2 = ([(0.5 kg + 3 * 25 kg) × 9.8 m/s^2 × 3.8m) / (0.5 kg)]

Finally, we take the square root of both sides to find the velocity:

velocity = √([(0.5 kg + 3 * 25 kg) × 9.8 m/s^2 × 3.8m) / (0.5 kg)]

Evaluating this expression will give us the maximum velocity reached by the cantaloupe.