Suppose a 1800-kg car passes over a bump in a roadway that follows the arc of a circle of radius 18.4 m as in the figure shown below.
(a) What force does the road exert on the car as the car passes the highest point of the bump if the car travels at 9.24 m/s? (Neglect any friction that may occur.)
magnitude
im getting 8352.156N but it is incorrect i did 1800*9.24^2/18.4 and i got 8352.156N
no this is the correct answer :
N = ma= mg- mv²/R=
1800•9.8-1800•9.24²/18.4 =9287.84 N
N = ma= mg+ mv²/R=1800•9.8+ 1800•9.24²/18.4 =9792.16 N
To determine the force exerted by the road on the car as it passes the highest point of the bump, we need to consider the forces acting on the car. The main force at play is the force of gravity acting vertically downwards on the car.
At the highest point of the bump, there are two forces acting on the car: the gravitational force (mg) and the normal force (N) exerted by the road. These forces must add up to provide the centripetal force required to keep the car moving in a circle.
The centripetal force is given by the equation:
F_c = (mv^2) / r
where:
F_c = centripetal force
m = mass of the car
v = velocity of the car
r = radius of the circular path
Plugging in the given values:
m = 1800 kg
v = 9.24 m/s
r = 18.4 m
F_c = (1800 kg * (9.24 m/s)^2) / 18.4 m = 8352.156 N
Therefore, your calculation is correct. The force exerted by the road on the car at the highest point of the bump is indeed 8352.156 N.
To find the correct answer, we need to consider the forces acting on the car at the highest point of the bump. At the top of the bump, the car is in dynamic equilibrium, which means that the net force acting on it is zero.
The forces acting on the car at the top of the bump are gravity (mg) acting vertically downward and the normal force (N) acting perpendicular to the surface of the road. Since the car is not accelerating vertically, the magnitudes of these two forces must be equal.
We can start by calculating the weight of the car using the formula weight = mass * gravitational acceleration (W = mg). The mass of the car is given as 1800 kg and the gravitational acceleration is approximately 9.8 m/s^2. So, the weight of the car is:
W = 1800 kg * 9.8 m/s^2 = 17,640 N
Since the normal force is equal in magnitude and opposite in direction to the weight of the car at the highest point, the normal force is also 17,640 N.
Therefore, the road exerts a force of 17,640 N on the car as it passes the highest point of the bump.