It takes 222 kJ of work to accelerate a car from 22.1 m/s to 29.9 m/s. What is the car's mass?
To find the car's mass, we can apply the work-energy principle. The work done on an object is equal to the change in its kinetic energy. In this case, the work done is 222 kJ (kilojoules).
The formula for kinetic energy is:
KE = 1/2 * m * v^2
Where KE is the kinetic energy, m is the mass, and v is the velocity.
First, we need to convert the work done from kilojoules to joules, as the unit of kinetic energy is in joules. One kilojoule (kJ) is equal to 1000 joules (J). So, 222 kJ is equal to 222,000 J.
Next, we can calculate the initial and final kinetic energy using the given velocities:
KE_initial = 1/2 * m * v_initial^2
KE_final = 1/2 * m * v_final^2
Since the work done is equal to the change in kinetic energy, we have:
Work = KE_final - KE_initial
Substituting the formulas for the kinetic energies, we get:
222,000 J = 1/2 * m * v_final^2 - 1/2 * m * v_initial^2
Now, we can rearrange the equation to solve for the mass (m):
222,000 J = 1/2 * m * (v_final^2 - v_initial^2)
Multiply both sides by 2 to eliminate the 1/2:
444,000 J = m * (v_final^2 - v_initial^2)
Divide both sides by (v_final^2 - v_initial^2):
m = 444,000 J / (v_final^2 - v_initial^2)
Now, we can plug in the values:
v_initial = 22.1 m/s
v_final = 29.9 m/s
Calculating the values, we get:
m = 444,000 J / (29.9^2 - 22.1^2)
= 444,000 J / (894.01 - 488.41)
= 444,000 J / (405.6)
= 1095.63 kg
Therefore, the car's mass is approximately 1096 kg.