It takes 170 kJ of work to accelerate a car from 21.5 m/s to 27.0 m/s. What is the car's mass?
Work = change in KE so
170e3 = 1/2mv2^2 - 1/2mv1^2
Solve for m using the two v's v1 & v2
To find the mass of the car, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.
The work done on the car can be calculated using the formula:
Work = (1/2) * mass * (final velocity^2 - initial velocity^2)
Let's substitute the given values into the formula:
170 kJ = (1/2) * mass * (27.0 m/s)^2 - (21.5 m/s)^2
First, let's convert the work from kilojoules to joules:
170 kJ = 170 * 1000 J
Now, let's simplify the equation:
170,000 J = (1/2) * mass * (729 - 462.25)
170,000 J = (1/2) * mass * 266.75
Next, we can multiply both sides of the equation by 2 to cancel out the fraction:
340,000 J = mass * 266.75
Finally, we can isolate the mass by dividing both sides of the equation by 266.75:
mass = 340,000 J / 266.75
mass ≈ 1273.97 kg
Therefore, the mass of the car is approximately 1273.97 kg.