Final answer:
To find the total static friction force on a decelerating car traveling along a curve, one must calculate the centripetal force and the deceleration force, consider them as vectors, take their vector sum to get the total friction force, and then express this force as a fraction of the car's weight.
Step-by-step explanation:
The question revolves around calculating the static friction force acting on a car as it travels and decelerates on a curved path. To find this, we have to consider both the centripetal force required to keep the car moving along the curve and the force due to the car's deceleration.
Step-by-Step Solution
The centripetal force (Fc) needed to keep the car on the curve is given by the formula:
Fc = (m*v^2) / r
where:
- m is the mass of the car (1200 kg),
- v is the speed of the car (10 m/s), and
- r is the radius of the curve (250 m).
The deceleration force (Fd) is given by Newton's second law:
Fd = m*a
where:
- a is the deceleration rate (2 m/s²).
To find the total static friction force, we need to calculate the vector sum of Fc and Fd, taking into account that these forces are perpendicular to each other. Therefore, the total friction force (Ft) is:
Ft = √(Fc^2 + Fd^2)
The weight of the car (W) is:
W = m*g
where g is the acceleration due to gravity (9.81 m/s²).
Now, we find the fraction of the friction force to the car's weight:
Fraction = Ft / W
Examples such as these help in understanding how forces act on a car in motion and the role of friction in such dynamic situations. In real-world scenarios, this knowledge is crucial for ensuring vehicle stability and safety.