It takes 226 kJ of work to accelerate a car from 23.3 m/s to 28.3 m/s. What is the car's mass?
Ignoring dissipative losses (air resistance, friction, etc.),
difference of kinetic energy equals work done,
=>
(1/2)m(28.3^2-23.3^2)=226000 j
Solve for m.
To find the car's mass, we can use the equation for work:
Work = Force x Distance x cos(θ)
In this case, the work is given as 226 kJ, which can be converted to joules (J) by multiplying by 1000 since 1 kJ = 1000 J.
So, Work = 226,000 J.
The force can be calculated using Newton's second law:
Force = Mass x Acceleration
Since the car is accelerating, we need to calculate the net force acting on the car.
The net force (F_net) can be found using the equation:
F_net = (1/2) x Mass x (final velocity^2 - initial velocity^2)
Where:
- Mass is the car's mass (what we want to find)
- Final velocity is the final velocity of the car (28.3 m/s)
- Initial velocity is the initial velocity of the car (23.3 m/s)
We can rearrange the equation to solve for the car's mass:
Mass = 2 x (Work / ((final velocity^2) - (initial velocity^2)))
Plugging in the known values:
Mass = 2 x (226,000 / ((28.3^2) - (23.3^2)))
Now, let's calculate the car's mass.