Calculate the kinetic energy of a 150 g baseball moving at a speed of 38 m/squat (85mph)
The correct answer and explanation is:
The kinetic energy of an object can be calculated using the formula: KE=12mv2KE = \frac{1}{2} m v^2
Where:
- KEKE is the kinetic energy,
- mm is the mass of the object,
- vv is the velocity of the object.
Step 1: Convert the mass into kilograms.
Since the mass of the baseball is given in grams (150 g), we need to convert it to kilograms: 150 g=0.150 kg150 \, \text{g} = 0.150 \, \text{kg}
Step 2: Use the given velocity.
The velocity of the baseball is 38 m/s. This is already in SI units, so no conversion is necessary.
Step 3: Substitute the values into the formula.
Now, substitute the mass m=0.150 kgm = 0.150 \, \text{kg} and velocity v=38 m/sv = 38 \, \text{m/s} into the formula: KE=12×0.150×(38)2KE = \frac{1}{2} \times 0.150 \times (38)^2
Step 4: Calculate the kinetic energy.
First, square the velocity: 382=1444 m2/s238^2 = 1444 \, \text{m}^2/\text{s}^2
Now, multiply by the mass and divide by 2: KE=12×0.150×1444=0.075×1444=108.3 JKE = \frac{1}{2} \times 0.150 \times 1444 = 0.075 \times 1444 = 108.3 \, \text{J}
Final Answer:
The kinetic energy of the baseball is 108.3 joules (J).
Explanation:
Kinetic energy is the energy that an object possesses due to its motion. The formula 12mv2\frac{1}{2} m v^2 shows that kinetic energy depends on both the mass and the speed of the object. In this case, the mass of the baseball is relatively small, but it still has significant kinetic energy because of its speed. The faster the object moves, the greater the kinetic energy. This is why high-speed objects, like baseballs thrown or hit with high velocity, can have considerable energy despite their small mass. The kinetic energy of a baseball moving at 38 m/s (85 mph) is enough to allow it to travel significant distances, which is why it’s critical in sports like baseball.