a gun converts 200J of stored energy into kinetic energy of the 0.02kg bullet. a)What is the speed of the bullet as it leaves the gun? b)If the gun is fired straight up, how high will the bullet go?
a)200J
b)m*g*h= (0.02kg)(10m/s^2)=200J
h=100m
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. We know that the gun converts 200J of stored energy into kinetic energy of the 0.02kg bullet.
a) The kinetic energy formula is given as KE = 1/2 * m * v^2, where KE is the kinetic energy, m is the mass, and v is the velocity (speed) of the bullet.
In this case, we can set up the equation as follows:
200J = 1/2 * 0.02kg * v^2
Let's solve for v. Rearranging the equation, we have:
v^2 = (200J * 2) / (0.02kg)
v^2 = 20000J / 0.02kg
v^2 = 1000000 m^2/s^2
Taking the square root of both sides, we find:
v = √(1000000 m^2/s^2)
v = 1000 m/s
Therefore, the speed of the bullet as it leaves the gun is 1000 m/s.
b) If the gun is fired straight up, the bullet will experience the force of gravity acting in the opposite direction, slowing it down until it eventually comes to a stop and starts to fall back down.
To find the height the bullet reaches, we can use the principle of conservation of mechanical energy, which states that the initial mechanical energy is equal to the final mechanical energy.
The mechanical energy consists of potential energy (PE) and kinetic energy (KE). At the highest point, when the bullet momentarily comes to a stop, all of the initial kinetic energy is converted into potential energy.
The potential energy formula is given as PE = m * g * h, where m is the mass, g is the acceleration due to gravity (approximately 10m/s^2 on Earth), and h is the height.
In this case, we can set up the equation as follows:
200J = 0.02kg * 10m/s^2 * h
Simplifying the equation, we have:
200J = 0.2kg * h
Solving for h, we find:
h = 200J / (0.2kg)
h = 1000 m
Therefore, if the gun is fired straight up, the bullet will reach a height of 1000 meters before it starts to fall back down.