Compression Distance of a Trampoline Calculation
How to calculate the compression distance of a trampoline when a child jumps on it?
Given the mass of the child, the spring constant, and the height above the trampoline, how can we determine the compression distance?
Answer:
To find the compression distance of the trampoline, we can use Hooke's law, which states that the force exerted by a spring is directly proportional to its displacement. In this case, the spring constant is given as 5200 N/m. The weight of the child can be calculated using the formula weight = mass x acceleration due to gravity. The displacement of the trampoline can then be found using the formula force = spring constant x displacement. Rearranging the equation, we get displacement = force / spring constant. Plugging in the values, we have displacement = weight / spring constant.
Given that the mass of the child is 30 kg and the acceleration due to gravity is 9.8 m/s^2, we can calculate the compression distance as follows:
- Convert the mass to weight: weight = mass x acceleration due to gravity = 30 kg x 9.8 m/s^2 = 294 N
- Calculate the displacement: displacement = weight / spring constant = 294 N / 5200 N/m = 0.05654 m
- Convert the displacement to centimeters: displacement = 0.05654 m x 100 cm/m = 5.654 cm
Therefore, the compression distance of the trampoline when a child weighing 30 kg jumps on it is approximately 5.654 centimeters.