A 25 kg child bounces on a pogo stick.
The pogo stick has a spring with spring constant 2.0*10^4 N/m. When the child makes a nice big bounce, he finds that at the bottom of the bounce he is accelerating upwards at 9.8 m/s^2. How much is the spring compressed?
you need to multiply 0.0245 by 100 to convert m to cm to get a final answer of 2.5 cm to two significant figures
its not .0245
To find out how much the spring is compressed, we can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.
Hooke's Law can be expressed as:
F = k * x
Where:
F is the force exerted by the spring,
k is the spring constant,
x is the displacement of the spring from its equilibrium position.
In this case, the child is accelerating upwards at 9.8 m/s^2, which means the net force acting on the child is equal to the force exerted by the spring.
The net force acting on the child can be calculated using Newton's second law of motion:
F_net = m * a
Where:
F_net is the net force acting on the child,
m is the mass of the child,
a is the acceleration of the child.
By equating the two forces, we have:
m * a = k * x
Substituting the given values:
m = 25 kg
a = 9.8 m/s^2
k = 2.0 * 10^4 N/m
We can rearrange the equation to solve for x:
x = (m * a) / k
x = (25 kg * 9.8 m/s^2) / (2.0 * 10^4 N/m)
Calculating the expression:
x = 0.0125 m or 12.5 cm
Therefore, the spring is compressed by 12.5 cm.
kx - mg = ma
2*10^4 x = 25 (9.8+9.8)