On a highway curve with radius 30 m, the maximum force of static friction (centripetal force) that can act on a 1,423-kg car going around the curve is 8,127 n. what speed limit should be posted for the curve so that cars can negotiate it safely?

Answers

Answer 1

Answer: To determine the speed limit for the curve, we can use the centripetal force equation. The centripetal force (Fc) is given by the equation Fc = (m * v^2) / r, where m is the mass of the car, v is the velocity, and r is the radius of the curve.

In this case, the maximum force of static friction acting as the centripetal force is given as 8,127 N, the mass of the car is 1,423 kg, and the radius of the curve is 30 m.

We can rearrange the equation to solve for the velocity (v):

v = sqrt((Fc * r) / m)

Now, let's substitute the given values into the equation:

v = sqrt((8,127 N * 30 m) / 1,423 kg)

v ≈ 13.57 m/s

Therefore, to ensure that cars can negotiate the curve safely, the speed limit should be posted at approximately 13.57 m/s (or about 49 km/h). It's important to note that this is only a rough estimate, and other factors such as road conditions and driver behavior should also be taken into consideration when setting speed limits.

Answer 2

Answer:

Final answer:

The speed at which a car can safely navigate a given curve is determined by the equation for centripetal force and the maximum static friction that prevents the car from slipping. Calculating this speed using the given force of static friction (8,127 N), mass of the car (1,423 kg) and the radius of the curve (30 m), we get a result of roughly 22.6 m/s or 81.4 km/h.

Explanation:

The problem involves finding the speed at which a car can safely navigate a highway curve without slipping, given a set radius and maximum force of static friction. This is a physics scenario involving centripetal force and friction. Centripetal force is the net force causing circular motion and static friction is the friction that acts to prevent the car from slipping off the road.

In this scenario, the maximum static friction matches the required centripetal force for a safe curve negotiation. Hence, the equation for centripetal force, Fc = mv²/r, applies here. In this expression, Fc is the centripetal force, m is the mass of the car, v is the velocity or speed, and r is the radius of the curve. Given that Fc = 8,127N, m = 1,423 kg, and r = 30 m, we can rearrange the formula to find v = √(Fc ∗ r / m).

Running the calculation, v = √((8,127 N * 30m) / 1,423 kg), results in a speed limit of roughly 22.6 m/s. However, as speed limits are not posted in meters per second, it is appropriate to convert the speed to kilometers per hour. Multiply the result by (3600 s/h / 1000 m/km) to convert it into km/h which gives a speed limit of about 81.4 km/h.

Learn more about Centripetal Force and Friction here:

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