91Ó°ÊÓ

To understand kinetic energy and how to calculate it, it's essential to first grasp the physics equations involved. The key equation here is:\[ KE = \frac{1}{2} mv^2 \] This equation states that kinetic energy (KE) is equal to one-half the mass (m) of an object multiplied by the square of its velocity (v). This formula captures the relationship between an object's mass, its speed, and the resulting energy due to its motion. Every time you see a physics problem involving motion and energy, this equation will often come into play. Remember, mass must be in kilograms (kg) and velocity in meters per second (m/s). Getting comfortable with this formula will make problems involving kinetic energy much more manageable.

• Mass \(m\) should always be in kilograms.
• Velocity \(v\) should always be in meters per second.
• Kinetic energy \(KE\) will be in Joules (J).

Unit conversion is a critical step in solving physics problems. Often, the given values are not in the standard SI units, so converting them is necessary. For instance, in the given problem:

• A mass of 4.2 grams needs to be converted to kilograms by dividing by 1000, so \[ 4.2 \, \text{g} = 0.0042 \, \text{kg} \].
• To convert 32 knots to meters per second, you need to multiply by 0.51444 (since one knot is 0.51444 m/s), thus \[ 32 \, \text{knots} \approx 16.5 \, \text{m/s} \].

Unit conversion makes sure that all values are compatible with the physics equations, keeping the calculations accurate. Always double-check your units; incorrect units can lead to incorrect results.

Now that we understand the physics equation and have converted all units appropriately, we can proceed to calculate the kinetic energy for each object. First, let's recall the kinetic energy formula: \[ KE = \frac{1}{2} mv^2 \] Plugging in the values:

• For the football linebacker: mass = 110 kg and velocity = 8.1 m/s: \[ KE = \frac{1}{2} \times 110 \times (8.1)^2 \] simplifying, \[ KE = 0.5 \times 110 \times 65.61 \ KE = 3608.55 \ J \]
• For the bullet: mass = 0.0042 kg and velocity = 950 m/s: \[ KE = \frac{1}{2} \times 0.0042 \times (950)^2 \] simplifying, \[ KE = 0.5 \times 0.0042 \times 902500 \ KE = 1895.25 \ J \]
• For the aircraft carrier: mass = 40.2 \times 10^8 kg and velocity = 16.5 m/s: \[ KE = \frac{1}{2} \times 40.2 \times 10^8 \times (16.5)^2 \] simplifying, \[ KE = 0.5 \times 40.2 \times 10^8 \times 272.25 \ KE = 5.47035 \times 10^{10} \ J \]

Summarizing the results:

• The kinetic energy of the football linebacker is 3608.55 J.
• The kinetic energy of the bullet is 1895.25 J.
• The kinetic energy of the aircraft carrier is 5.47035 × 10^{10} J.

Understanding each step and performing the necessary calculations accurately ensures that we find the correct kinetic energy for each object. Practice more to master these calculations!