a gun converts 200J of stored energy into kinetic energy of the 0.02kg bullet. What is the speed of the bullet as it leaves the gun? If the gun is fired straight up, how high will the bullet go?
See previous post: Thu, 4-23-15, 6:12 PM
To find the speed of the bullet as it leaves the gun, we can use the principle of conservation of energy. The stored energy in the gun is converted entirely into the kinetic energy of the bullet.
1. Calculate the kinetic energy of the bullet:
The formula for kinetic energy is given by:
KE = 1/2 * m * v^2
Where:
KE = kinetic energy
m = mass of the bullet (0.02 kg)
v = velocity of the bullet (unknown)
Since we know the energy converted is 200 J, we set up the equation:
200 J = 1/2 * 0.02 kg * v^2
2. Solve for the velocity of the bullet:
Rearranging the equation, we get:
v^2 = (2 * 200 J) / 0.02 kg
v^2 = 20000 m^2/s^2
Taking the square root of both sides:
v = √(20000) m/s
Calculating the square root, we find:
v ≈ 141.42 m/s
So, the speed of the bullet as it leaves the gun is approximately 141.42 m/s.
To find out how high the bullet will go if the gun is fired straight up, we can use the concept of projectile motion and the fact that the height reached will be equal to the potential energy at that point.
3. Calculate the height reached by the bullet:
The potential energy when the bullet reaches its maximum height is equal to the initial kinetic energy of the bullet.
Therefore, the equation becomes:
Potential Energy = 1/2 * m * v^2
Potential Energy = 1/2 * 0.02 kg * (141.42 m/s)^2
4. Solve for the height:
Potential Energy = 1/2 * 0.02 kg * (141.42 m/s)^2
Potential Energy = 0.02 kg * 141.42^2 m^2/s^2
Converting the potential energy back to height, we can use the equation:
Potential Energy = m * g * h
Where:
m = mass of the bullet (0.02 kg)
g = acceleration due to gravity (9.8 m/s^2)
h = height reached by the bullet (unknown)
Rearranging the equation, we get:
h = Potential Energy / (m * g)
h ≈ (0.02 kg * 141.42^2 m^2/s^2) / (0.02 kg * 9.8 m/s^2)
Simplifying the equation, we find:
h ≈ 141.42^2 / 9.8 m
h ≈ 2016.53 m
Therefore, if the gun is fired straight up, the bullet will reach a height of approximately 2016.53 meters.