A car travels around an unbanked highway curve (radius 0.15 km) at a constant speed of 25 m/s. What is the magnitude of the resultant force acting on the driver, who weighs 0.8kN?
Centripetal force f = mV²/r = mrω²
ω is angular velocity in radians/sec
1 radian/sec = 9.55 rev/min
m is mass in kg
r is radius of circle in meters
V is the tangental velocity in m/s
f is in Newtons
m = w/g = 800/9.8 = 81.6 kg
F = mV²/r = 81.6(25)² / (150) = 340 N
To find the magnitude of the resultant force acting on the driver, we need to consider the forces at play. In this situation, the main forces involved are the gravitational force acting downwards and the centripetal force acting towards the center of the curve.
First, let's determine the centripetal force using the formula:
F_centripetal = (m * v^2) / r
where:
m is the mass of the driver (given as 0.8 kN, which is equivalent to 800 N),
v is the velocity of the car (25 m/s), and
r is the radius of the curve (0.15 km, which is equivalent to 150 m).
Plugging in the values, we get:
F_centripetal = (800 N * (25 m/s)^2) / 150 m
Calculating this equation gives us:
F_centripetal = 33,333.33 N
Now, since the gravitational force is directly acting downwards, it can be calculated simply as the weight of the driver, which is given as 0.8 kN, or 800 N.
Therefore, the magnitude of the resultant force acting on the driver is the vector sum of the centripetal force and the gravitational force:
Resultant force magnitude = F_centripetal + F_gravitational
= 33,333.33 N + 800 N
= 34,133.33 N
So, the magnitude of the resultant force acting on the driver is 34,133.33 N.