A drag racing car starting from a standstill can reach a speed of 320 km/h in 6.50s by exerting an average horizontal force of 1.52x10^4 N on the pavement. If friction equals 5.2x10^3 N, what is the mass of the car?
To find the mass of the car, we can use Newton's second law of motion, which states that the force exerted on an object is equal to the mass of the object multiplied by its acceleration. In this case, we're given the force exerted by the car and the friction force, so we can calculate the net force acting on the car.
First, let's find the net force:
Net force = Applied Force - Friction Force
Net force = 1.52x10^4 N - 5.2x10^3 N
Net force = 1.52x10^4 N - 5.2x10^3 N
Net force = 9x10^3 N
Now, let's calculate the acceleration of the car using the formula:
Net force = mass × acceleration
Rearranging the formula, we have:
Acceleration = Net force / mass
Plugging in the values, we get:
9x10^3 N = mass × acceleration
Next, we need to calculate the acceleration of the car. We know that the car starts from rest and reaches a final speed of 320 km/h, which is equivalent to 88.9 m/s.
Using the formula:
Acceleration = Change in velocity / Time taken
Rearranging the formula, we have:
Change in velocity = Acceleration × Time taken
Plugging in the values, we get:
88.9 m/s = Acceleration × 6.50 s
Now, let's solve for acceleration:
Acceleration = 88.9 m/s / 6.50 s
Acceleration = 13.7 m/s^2
Now, substituting the acceleration back into the previous equation, we have:
9x10^3 N = mass × 13.7 m/s^2
Finally, to solve for the mass:
mass = 9x10^3 N / 13.7 m/s^2
mass ≈ 657 kg
Therefore, the mass of the car is approximately 657 kg.