What speed would a fly with a mass of 0.71 g need in order to have the same kinetic energy as a 1250 kg automobile traveling at a speed of 11 m/s?
To find the speed at which a fly with a mass of 0.71 g would need to have the same kinetic energy as a 1250 kg automobile traveling at a speed of 11 m/s, we can use the formula for kinetic energy:
Kinetic Energy = 1/2 * mass * velocity^2
Let's first convert the mass of the fly from grams to kilograms:
0.71 g = 0.71 * 10^-3 kg
Now we can calculate the kinetic energy of the automobile using the given mass and velocity:
Kinetic Energy of automobile = 1/2 * 1250 kg * (11 m/s)^2
Next, we can set the kinetic energy of the fly equal to the kinetic energy of the automobile and solve for its velocity:
1/2 * (0.71 * 10^-3 kg) * velocity_fly^2 = 1/2 * 1250 kg * (11 m/s)^2
Simplifying the equation:
0.355 * 10^-3 kg * velocity_fly^2 = 76250 kg * m^2/s^2
Dividing both sides by 0.355 * 10^-3 kg:
velocity_fly^2 = (76250 kg * m^2/s^2) / (0.355 * 10^-3 kg)
velocity_fly^2 ≈ 215493,039 m^2/s^2
Taking the square root of both sides:
velocity_fly ≈ √(215493,039 m^2/s^2)
velocity_fly ≈ 464.54 m/s (rounded to two decimal places)
Therefore, in order to have the same kinetic energy as the automobile, the fly would need to be traveling at approximately 464.54 m/s.
To find the speed of the fly, we need to equate its kinetic energy to that of the automobile.
The formula for kinetic energy is given by:
K.E. = (1/2) * m * v^2
Where K.E. represents kinetic energy, m represents mass, and v represents velocity.
Let's calculate the kinetic energy of the automobile:
K.E. of automobile = (1/2) * m_automobile * v_automobile^2
= (1/2) * 1250 kg * (11 m/s)^2
Now, let's calculate the kinetic energy of the fly using the given mass (0.71 g = 0.00071 kg):
K.E. of fly = (1/2) * m_fly * v_fly^2
= (1/2) * 0.00071 kg * v_fly^2
Since we want the kinetic energy of the fly to be equal to that of the automobile, we have:
(1/2) * 1250 kg * (11 m/s)^2 = (1/2) * 0.00071 kg * v_fly^2
Now we can solve for the velocity of the fly, v_fly:
v_fly = sqrt((1250 kg * (11 m/s)^2) / (0.00071 kg))
Calculating this using a calculator, we find:
v_fly ≈ 560,561 m/s
Therefore, the fly would need a speed of approximately 560,561 m/s to have the same kinetic energy as the 1250 kg automobile traveling at a speed of 11 m/s.