It takes 180 kJ of work to accelerate a car from 21.0 m/s to 27.5 m/s. What is the car's mass?
kg?
Initial kinetic energy
= (1/2)mv0²
Final kinetic energy
= (1/2)mv1²
Difference
E = (1/2)m(v1²-v0²)
Solve for m
hi
To find the mass of the car, you can use the principle of work-energy. The work done on the car is equal to its change in kinetic energy.
The work done on the car is given as 180 kJ (kilojoules), which can be converted to joules (J) by multiplying by 1000:
180 kJ = 180,000 J
The change in kinetic energy is equal to the final kinetic energy minus the initial kinetic energy:
ΔKE = KE_final - KE_initial
The formula for kinetic energy is given by:
KE = (1/2) * m * v^2
Substituting the initial and final velocities:
ΔKE = (1/2) * m * v_final^2 - (1/2) * m * v_initial^2
Plugging in the given values:
ΔKE = (1/2) * m * (27.5 m/s)^2 - (1/2) * m * (21.0 m/s)^2
Now we can solve for the mass (m) of the car.
180,000 J = (1/2) * m * (27.5 m/s)^2 - (1/2) * m * (21.0 m/s)^2
To simplify the equation, we can calculate the square of the velocities:
180,000 J = (1/2) * m * 756.25 m^2/s^2 - (1/2) * m * 441.00 m^2/s^2
Now we can combine like terms:
180,000 J = (1/2) * m * (756.25 - 441.00) m^2/s^2
180,000 J = (1/2) * m * 315.25 m^2/s^2
To isolate the mass (m), we divide both sides of the equation by (1/2) * 315.25 m^2/s^2:
m = (180,000 J) / [(1/2) * 315.25 m^2/s^2]
m = (180,000 J) / (157.625 m^2/s^2)
Calculating this division gives us the mass of the car in kilograms (kg).