A 1.47-newton baseball is dropped from a height of 10.0 meters and falls through the air to the ground. The kinetic energy of the ball is 12.0 joules the instant before the ball strikes the ground. The maximum amount of mechanical energy converted to internal energy during the fall is_________.
PE-KE = 1.47*10 - 12 = 2.7
So, ...
To find the maximum amount of mechanical energy converted to internal energy during the fall, we need to calculate the initial mechanical energy of the ball and subtract it from the kinetic energy just before impact.
Step 1: Calculate the initial potential energy of the ball:
Potential energy (PE) = mass (m) x gravity (g) x height (h)
where the mass of the ball (m) can be calculated using the formula:
m = force (F) / acceleration due to gravity (g)
Since the weight of the ball is given as 1.47 newtons:
m = 1.47 N / 9.8 m/s^2
Step 2: Calculate the initial potential energy of the ball using the formula:
PE = m x g x h
where g is the acceleration due to gravity (9.8 m/s^2) and h is the height (10.0 meters).
Step 3: Calculate the initial kinetic energy of the ball by subtracting the potential energy from the kinetic energy just before impact:
Initial kinetic energy (KE) = Kinetic energy just before impact (KE_final) - Potential energy (PE)
Step 4: The maximum amount of mechanical energy converted to internal energy during the fall is equal to the initial kinetic energy of the ball.
Let's calculate it step by step:
Step 1:
m = 1.47 N / 9.8 m/s^2
Step 2:
PE = m x g x h
PE = (m) x (g) x (h)
Step 3:
Initial KE = KE_final - PE
Step 4:
Maximum amount of mechanical energy converted to internal energy = Initial KE
Now let's perform the calculations:
Step 1:
m = 1.47 N / 9.8 m/s^2
m ≈ 0.15 kg
Step 2:
PE = (m) x (g) x (h)
PE = (0.15 kg) x (9.8 m/s^2) x (10.0 m)
PE ≈ 14.7 J
Step 3:
Initial KE = KE_final - PE
12.0 J = KE_final - 14.7 J
KE_final ≈ 12.0 J + 14.7 J
KE_final ≈ 26.7 J
Step 4:
Maximum amount of mechanical energy converted to internal energy = Initial KE
Maximum amount of mechanical energy converted to internal energy ≈ 26.7 J
Therefore, the maximum amount of mechanical energy converted to internal energy during the fall is approximately 26.7 joules.
To find the maximum amount of mechanical energy converted to internal energy during the fall, we need to calculate the initial mechanical energy of the baseball (when it was dropped) and subtract the final mechanical energy of the ball (just before it strikes the ground) from it.
The mechanical energy of an object is a combination of its potential energy and kinetic energy.
1. Calculating the initial mechanical energy (when the ball was dropped):
The initial potential energy (PE) is given by the formula: PE = mgh, where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height.
PE = (mass) × (acceleration due to gravity) × (height)
The mass is not provided directly, but the weight (W = mg) is given, which is equal to 1.47 N. Since weight is equal to mass times acceleration due to gravity, we can rearrange the equation to find mass: m = W/g.
mass = 1.47 N / 9.8 m/s²
2. Calculating the final mechanical energy (just before the ball strikes the ground):
The final mechanical energy (KE) is given as 12.0 joules.
3. Determining the maximum amount of mechanical energy converted to internal energy:
Maximum converted mechanical energy = Initial mechanical energy – Final mechanical energy.
Since the mechanical energy is conserved during free-fall, the initial mechanical energy is equal to the final mechanical energy.
Maximum converted mechanical energy = Initial mechanical energy – Final mechanical energy
= Initial mechanical energy - KE
Substituting the values into the equation, you can calculate the maximum amount of mechanical energy converted to internal energy during the fall.