A road heading due east passes over a small hill. You drive a car of mass m at constant speed v over the top of the hill, where the shape of the roadway is well approximated as an arc of a circle with radius R. Sensors have been placed on the road surface there to measure the downward force that cars exert on the surface at various speeds. The table gives values of this force versus speed for your car is shown in (Figure 1) . Treat the car as a particle.

n vs. v^2

So what is the question? Where is the table?

897 kg

Explain pls

Well, if the car is treated as a particle, does that mean it starts belting out Bohemian Rhapsody when it hits top speed? Because that would definitely make things more interesting!

To analyze the situation described, we need to understand the relationship between the downward force exerted by the car on the road surface and its speed. The table provided shows the values of this force at different speeds.

From the information given, we can see that the road is shaped like an arc of a circle with radius R. This indicates that the car is moving on a curved path.

To find a function that relates the downward force to the speed, we can consider the forces acting on the car as it moves over the hill.

First, let's draw a free-body diagram:

N
__|__
| |
(m) |

Here, N represents the normal force exerted by the road on the car. Since the car is moving in a circular path, there must be a centripetal force acting towards the center of the circle. We can represent this force as Fc.

The net force in the vertical direction is the difference between the downward force W (weight) and the upward force N:

Net force = W - N

Since the car is moving at a constant speed, the net force in the vertical direction must be zero. Therefore:

W - N = 0

Since the weight, W, is given by W = mg, where m is the mass of the car and g is the acceleration due to gravity, we can rewrite the equation as:

mg - N = 0

From this equation, we can see that the normal force N is equal to the weight of the car, mg, when the car is moving at a constant speed on a level surface.

However, in this case, the car is moving on a curved path. Due to the circular motion, there is an additional force called the centripetal force, Fc, which is directed towards the center of the circle.

The centripetal force is given by Fc = m * v^2 / R, where v is the speed of the car and R is the radius of the circle.

Therefore, the downward force exerted by the car on the road surface can be expressed as:

N = mg + m * v^2 / R

Now, let's examine the provided table of values for the downward force versus speed. By looking at the table, you can identify specific data points where the downward force is measured at different speeds for your car.

You can use these data points to plot a graph of downward force versus speed. By fitting a curve to the data points, you can determine the relationship between the two variables.

To summarize, the downward force exerted by the car on the road surface depends on its speed and is given by N = mg + m * v^2 / R. By using the provided table of values, you can plot a graph and analyze the relationship between the two variables.

how did you get any of these answers im so confused