When a man, who weighs 650 N, stands on a particular trampoline, its springy surface shifts downward 0.1 m. If he bounces on it so that its surface shifts downward 0.28 m, how hard is it pushing up on him?
1219
N / m x 2nd m = answer
To determine how hard the trampoline is pushing up on the man, we can use Hooke's Law, which states that the force exerted by a spring is proportional to the displacement from its equilibrium position. The formula for Hooke's Law is:
F = k * x
where F is the force, k is the spring constant, and x is the displacement.
Given that the man's weight (force of gravity) is 650 N, and the trampoline's surface shifted downward by 0.1 m, we can calculate the spring constant (k) using the formula:
k = F / x
Substituting the known values:
k = 650 N / 0.1 m = 6500 N/m
Now, for the second scenario where the surface shifts downward by 0.28 m, we can calculate the force exerted by the trampoline using the same formula:
F = k * x
Substituting the known values:
F = 6500 N/m * 0.28 m = 1820 N
Therefore, the trampoline is pushing up on the man with a force of 1820 N.
The trampoline force is proportional to displacement, and in the opposite direction from the displacement. That is sometimes called Hooke's Law.
The answer is 2.8 times his weight.
2.8 * 650 = ___ N