a gun fires a 3g bullet with a speed of 400m/s. the gun barrel is 20cm long. how much energy is given to the bullet?
barrel length is not a factor
kinetic energy = 1/2 * .003 * 400^2
units are Joules
Need solutions
To determine the energy given to the bullet, we can use the formula for kinetic energy.
The formula for kinetic energy is:
KE = (1/2) mv^2
where KE is the kinetic energy, m is the mass of the bullet, and v is the velocity of the bullet.
Given:
Mass of the bullet (m) = 3 grams = 0.003 kg
Velocity of the bullet (v) = 400 m/s
First, let's find the kinetic energy:
KE = (1/2) * m * v^2
= (1/2) * 0.003 kg * (400 m/s)^2
Now, let's calculate the kinetic energy:
KE = (1/2) * 0.003 kg * (400 m/s)^2
= 0.0009 kg * (160,000 m^2/s^2)
= 144 J
Therefore, the energy given to the bullet is 144 Joules.
To calculate the energy given to the bullet, we need to use the equation for kinetic energy.
The formula for kinetic energy is given by:
KE = (1/2) * m * v^2
Where:
KE is the kinetic energy,
m is the mass of the object,
v is the velocity of the object.
In this case, the mass of the bullet is 3 g, which is equal to 0.003 kg, and the velocity is 400 m/s.
First, let's convert the length of the gun barrel from centimeters to meters. The length of the gun barrel is 20 cm, which is equal to 0.2 m.
The average force exerted on the bullet can be calculated using the following equation of motion:
F = m * a
Where:
F is the force exerted,
m is the mass of the object,
a is the acceleration.
In this case, the acceleration can be determined by calculating the change in velocity divided by the change in time.
The change in velocity can be calculated as:
Δv = v - u
Where:
Δv is the change in velocity,
v is the final velocity,
u is the initial velocity.
Since the bullet starts from rest inside the barrel, the initial velocity is 0 m/s. Therefore:
Δv = v - u
Δv = 400 m/s - 0 m/s
Δv = 400 m/s
The change in time can be determined by calculating the time taken for the bullet to travel the length of the barrel.
The average speed can be calculated using the equation:
v_avg = (u + v) / 2
Where:
v_avg is the average speed,
u is the initial velocity,
v is the final velocity.
Since the initial velocity is 0 m/s, the equation simplifies to:
v_avg = v / 2
v_avg = 400 m/s / 2
v_avg = 200 m/s
The time taken to travel the length of the barrel can be calculated as:
t = d / v_avg
Where:
t is the time taken,
d is the distance.
In this case, the distance is the length of the gun barrel, which is 0.2 m.
t = 0.2 m / 200 m/s
t = 0.001 s
Now, we can calculate the acceleration:
a = Δv / t
a = 400 m/s / 0.001 s
a = 400000 m/s^2
Next, let's calculate the force exerted on the bullet:
F = m * a
F = 0.003 kg * 400000 m/s^2
F = 1200 N
Now, we can calculate the energy given to the bullet using the kinetic energy equation:
KE = (1/2) * m * v^2
KE = (1/2) * 0.003 kg * (400 m/s)^2
KE = 0.6 J
Therefore, the amount of energy given to the bullet is 0.6 Joules.