A hand gun fires a 12.0 g bullet at a speed of 400 m/s.
What is its kinetic energy?
At what speed must a motorcycle of mass 173 kg move to have the same kinetic energy as the bullet? Express your answer in km/h.
K.E. is (1/2) M V^2
To get it in Joules, M must be in kg.
bullet KE = 960 Joules
If motorcycle KE = 960 J,and its mass is 173 kg,
(1/2)*173*Vm^2 = 960
then the motorcycle velocity is
Vm = 3.33 m/s
Convert that to km/h
To find the kinetic energy of an object, we can use the formula:
Kinetic energy (KE) = (1/2) * mass * velocity^2
1. For the first question, the mass of the bullet is given as 12.0 g, which is equivalent to 0.012 kg. The velocity of the bullet is 400 m/s.
Plugging the values into the formula, we get:
KE = (1/2) * 0.012 kg * (400 m/s)^2
Simplifying the equation:
KE = (1/2) * 0.012 kg * 160000 m^2/s^2
KE = 960 J
Therefore, the kinetic energy of the bullet is 960 Joules.
2. For the second question, we need to find the speed at which a motorcycle of mass 173 kg would have the same kinetic energy as the bullet.
Let's assume the speed of the motorcycle is v km/h. First, we need to convert this speed from km/h to m/s. Given that 1 km/h = 1/3.6 m/s, we can use this conversion factor.
Converting the speed of the motorcycle to m/s:
v m/s = (v km/h) * (1/3.6)
Now, we can find the kinetic energy of the motorcycle using the formula mentioned earlier:
KE = (1/2) * mass * velocity^2
Plugging in the values, we get:
KE = (1/2) * 173 kg * (v m/s)^2
Since we want the motorcycle to have the same kinetic energy as the bullet, we set the two equations equal to each other:
960 J = (1/2) * 173 kg * (v m/s)^2
Rearranging the equation:
(v m/s)^2 = (2 * 960 J) / (173 kg)
Taking the square root of both sides:
v m/s = sqrt((2 * 960 J) / (173 kg))
Now, we need to convert this speed back to km/h:
v km/h = (v m/s) * (3.6/1)
Calculating the value, we find:
v km/h ≈ 59.2 km/h
Therefore, the motorcycle must move at approximately 59.2 km/h to have the same kinetic energy as the bullet.