To calculate the total mechanical energy of the bullet, we need to consider both its kinetic energy and its gravitational potential energy.
1. Kinetic energy (KE):
The kinetic energy of an object is given by the equation KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.
Given:
- Mass of the bullet (m) = 0.50 g = 0.50/1000 = 0.00050 kg
- Velocity of the bullet (v) = 900 m/s
Using the formula, the kinetic energy of the bullet is:
KE = 1/2 * 0.00050 kg * (900 m/s)^2
KE = 1/2 * 0.00050 kg * 810,000 m^2/s^2
KE = 205 kg·m^2/s^2 (or J)
2. Gravitational potential energy (PE):
The gravitational potential energy is given by the equation PE = m * g * h, where m is the mass of the object, g is the acceleration due to gravity, and h is the height above the reference point (in this case, the ground).
Given:
- Mass of the bullet (m) = 0.00050 kg
- Height above the ground (h) = 1.5 m
- Acceleration due to gravity (g) = 9.8 m/s^2
Using the formula, the gravitational potential energy of the bullet is:
PE = 0.00050 kg * 9.8 m/s^2 * 1.5 m
PE = 0.00735 kg·m^2/s^2 (or J)
3. Total Mechanical Energy (TME):
The total mechanical energy of the bullet is the sum of its kinetic energy (KE) and gravitational potential energy (PE).
TME = KE + PE
TME = 205 kg·m^2/s^2 + 0.00735 kg·m^2/s^2
TME = 205.00735 kg·m^2/s^2 (or J)
Therefore, the total mechanical energy of the bullet is approximately 205.00735 J.
A 0.50g bullet is fired at 900m/s in a straight line 1.5m above ground. What is the total mechanical energy of the bullet?
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