Given the same exerted force (130N) exerted over 2s on two javelins of different mass (javelin1 = 1.2 kg; javelin2 = 1.6 kg), what is the kinetic energy of each javelin?
To find the kinetic energy of each javelin, we need to use the formula:
Kinetic energy (KE) = ½ * mass * velocity^2
First, we need to calculate the velocity of each javelin using the given force and time.
Step 1: Calculate the acceleration using Newton's second law of motion:
Force (F) = mass (m) * acceleration (a)
Rearranging the formula, we get:
Acceleration (a) = Force (F) / mass (m)
For javelin1:
Acceleration (a1) = 130 N / 1.2 kg
= 108.3 m/s^2
For javelin2:
Acceleration (a2) = 130 N / 1.6 kg
= 81.25 m/s^2
Step 2: Calculate the velocity using the obtained acceleration and time.
For javelin1:
Velocity (v1) = acceleration (a1) * time
= 108.3 m/s^2 * 2 s
= 216.6 m/s
For javelin2:
Velocity (v2) = acceleration (a2) * time
= 81.25 m/s^2 * 2 s
= 162.5 m/s
Step 3: Calculate the kinetic energy for each javelin using the formula mentioned above.
For javelin1:
Kinetic energy (KE1) = ½ * mass of javelin1 * velocity of javelin1^2
= ½ * 1.2 kg * (216.6 m/s)^2
≈ 56,452.31 Joules
For javelin2:
Kinetic energy (KE2) = ½ * mass of javelin2 * velocity of javelin2^2
= ½ * 1.6 kg * (162.5 m/s)^2
≈ 52,875 Joules
Therefore, the kinetic energy of javelin1 is approximately 56,452.31 Joules, and the kinetic energy of javelin2 is approximately 52,875 Joules.