Given: g=9.81 m/s square.
The parachute on a race car that weighs 8042 N opens at the end of a quarter-mile run when the car is traveling 35 m/s. What net retarding force must be supplied by the parachute to stop the car in a distance of 1020 m? Answer in units of N.
m = weight in Newtons/ 9.81
Change in kinetic energy = average force * distance.
The change in KE is all the KE, since it stopped.
(1/2) m v^2 at the start = F * 1020
So F = (1/2) m v^2 / 1020
To find the net retarding force required to stop the car, we can use the equation for acceleration:
Net force = mass × acceleration
We know the mass of the car from its weight. Weight is equal to mass multiplied by the acceleration due to gravity:
Weight = mass × acceleration due to gravity
Given that the weight of the car is 8042 N and the acceleration due to gravity is 9.81 m/s², we can calculate the mass of the car:
8042 N = mass × 9.81 m/s²
Rearranging the equation to solve for mass:
mass = 8042 N / 9.81 m/s²
Now we have the mass of the car. Next, we need to calculate the deceleration required to stop the car.
Deceleration is the change in velocity over time. We know the initial velocity of the car is 35 m/s, the final velocity is 0 m/s (since it comes to a stop), and the distance traveled is 1020 m.
Using the equation:
Final velocity² = Initial velocity² + 2 × acceleration × distance
Substituting the known values:
0² = 35² + 2 × acceleration × 1020
35² + 2 × acceleration × 1020 = 0
Now we can solve for acceleration:
Acceleration = (0 - 35²) / (2 × 1020)
Finally, we can calculate the net retarding force:
Net force = mass × acceleration
Plug in the values:
Net force = mass × [(0 - 35²) / (2 × 1020)]
Simplify the equation and calculate the net retarding force.