an .18 kg is placed a compressed spring on the floor. the springs exerts an average force of 2.8N through a distance of .15m as it shoots the ball upward. how high will the ball travel above the release spring?

To determine the height the ball will travel above the release spring, we can use the principles of work and energy conservation.

The work done by the spring force can be calculated using the formula:

Work (W) = force × distance

In this case, the spring exerts an average force of 2.8 N through a distance of 0.15 m. So, the work done by the spring force is:

W = 2.8 N × 0.15 m = 0.42 J

According to the principle of conservation of energy, this work done by the spring force is transferred into the potential energy of the ball when it reaches its maximum height. The potential energy (PE) can be calculated using the formula:

PE = m × g × h

Where:
m is the mass of the ball (0.18 kg)
g is the acceleration due to gravity (9.8 m/s²)
h is the height above the release spring that we want to find

By equating the work done by the spring force to the potential energy of the ball, we can solve for h:

0.42 J = 0.18 kg × 9.8 m/s² × h

Simplifying the equation:

0.42 J = 1.764 kg·m²/s² × h

Now, we can solve for h:

h = 0.42 J / (1.764 kg·m²/s²)
h ≈ 0.238 m

Therefore, the ball will travel approximately 0.238 meters (or 23.8 cm) above the release spring.

f=ma