18.6k views
1 vote
A circular curve of radius 150 m is banked at an angle of 15 degrees. A 750-kg car negotiates the curve at 85.0 km/h without skidding. a) what is the normal force on the tires exerted by the pavement. b) what is the frictional force exerted by the pavement on the tires?

User Niels Bom
by
7.2k points

2 Answers

2 votes

Final answer:

The normal and frictional forces on car tires during circular motion can be determined through the forces on an inclined plane equation and centripetal force calculation. For a car on a banked curve with no skidding, the frictional force can be assumed to be just enough to provide the needed centripetal force for the given conditions.

Step-by-step explanation:

To solve for the normal force and the frictional force exerted by the pavement on the tires, we'll apply physics principles involving circular motion and forces on an inclined plane. The car's mass is different from the examples, but we will use the same method to solve for the normal and frictional forces.



Normal Force

The normal force on the tires exerted by the pavement can be found by considering the components of the gravitational force parallel and perpendicular to the surface of the banked curve. Since we are given the car's mass (750 kg) and the banking angle (15 degrees), we can calculate the normal force using the equation for the forces on an inclined plane, taking into account the centripetal force required for circular motion.



Frictional Force

The frictional force on a banked curve is zero if no skidding occurs and the speed is ideal. However, if the speed is not at the ideal level, static friction will act towards the center of the curve to provide the necessary centripetal force. In this case, since the car is not skidding at 85 km/h, the frictional force can be assumed to be sufficient to provide the centripetal force without exceeding the maximum limit set by the coefficient of friction.



The car's speed, converted to m/s, and the radius of the curve are used to calculate the centripetal force, which, along with the angle of the curve and the car's weight, allows us to solve for the normal force and determine the conditions for no skidding, hence no need for a frictional force. If the car were to take the curve at less than the ideal speed, we would need to consider the static friction available as well.

User Satya Ranjan Sahoo
by
8.3k points
7 votes

Answer: a) 7.1 * 10^3 N; b) -880 N directed out of the curve.

Explanation: In order to solve this problem we have to use the Newton laws, then we have the following:

Pcos 15°-N=0

Psin15°-f= m*ac

from the first we obtain N, the normal force

N=750Kg*9.8* cos (15°)= 7.1 *10^3 N

Then to calculate the frictional force (f) we can use the second equation

f=P sin (15°) -m*ac where ac is the centripetal acceletarion which is equal to v^2/r

f= 750 *9.8 sin(15°)-750*(85*1000/3600)^2/150= -880 N

User Groceryheist
by
7.8k points