Final answer:
To find the velocity of the ball before it hits the foam, we use energy conservation. The potential energy at 2.0 meters is converted to kinetic energy just before impact. The calculated velocity just before the ball hits the foam is approximately 6.26 m/s.
Step-by-step explanation:
To determine how fast the steel ball is moving when it first hits the foam, we will use the principles of physics, specifically the conservation of energy. When the ball is dropped from a certain height, it has potential energy which is converted into kinetic energy just before the impact. We will ignore the small compression of the foam for the initial calculation, as we only need the speed at first contact.
The potential energy (PE) at the height of 2.0 meters can be calculated using the formula:
PE = m × g × h
Where:
- m is the mass of the ball (not given but not needed as it will cancel out)
- g is the acceleration due to gravity (approximately 9.81 m/s²)
- h is the height (2.0 meters)
The kinetic energy (KE) just before impact is equal to the potential energy at 2.0 meters because of the conservation of energy. The kinetic energy is given by:
KE = ½ × m × v²
Setting PE equal to KE and solving for v (velocity) gives:
m × g × h = ½ × m × v²
The mass (m) cancels out, and rearranging the formula to solve for v gives:
v = √(2 × g × h)
Substituting in the known values:
v = √(2 × 9.81 m/s² × 2.0 m)
v ≈ √(39.24 m²/s²)
v ≈ 6.26 m/s
Therefore, the velocity of the ball just before it hits the foam is approximately 6.26 m/s.