A 965 kg car is driving along a boardwalk. The car's center of mass is 45 cm in front of the rear wheels, and the distance between the front and rear wheels is 2 m. What total force does the car's front tires exert on the boardwalk? Give your answer in Newtons.
To find the total force exerted by the car's front tires on the boardwalk, we need to consider the weight distribution and the moment about the rear wheels.
First, let's calculate the weight of the car. The weight of an object can be found by multiplying its mass by the acceleration due to gravity (9.8 m/s^2).
Weight of the car = mass of the car x acceleration due to gravity
Weight of the car = 965 kg x 9.8 m/s^2
Weight of the car = 9467 N
Next, we need to determine the distribution of this weight between the front and rear tires. Since the car's center of mass is 45 cm in front of the rear wheels, the front tires bear a greater portion of the weight.
To calculate the weight on the rear tires, we can consider the moment about the rear wheels.
Moment = Force x Distance
The moment generated by the weight on the rear wheels is equal to the moment generated by the weight on the front wheels.
Moment about the rear wheels = Moment about the front wheels
Weight on the rear tires x rear wheels distance = Weight on the front tires x front wheels distance
Weight on the rear tires = (Weight of the car x front wheels distance) / total distance
Weight on the rear tires = (9467 N x 2 m) / (2 m + 45 cm)
Weight on the rear tires = 1939.13 N
Now, we can calculate the force exerted by the front tires on the boardwalk. Since the weight on the front tires is equal to the weight of the car minus the weight on the rear tires:
Force exerted by the front tires = Weight of the car - Weight on the rear tires
Force exerted by the front tires = 9467 N - 1939.13 N
Force exerted by the front tires = 7527.87 N (rounded to the nearest whole number)
Therefore, the total force exerted by the car's front tires on the boardwalk is approximately 7528 Newtons.