Derive an expression for maximum safety speed with which a vehicle should move along a curved horizontal road. state the significance of it.

Learning Objectives By the end of this section, you will be able to: • Explain the equation for centripetal acceleration • Apply Newton’s second law to develop the equation for centripetal force • Use circular motion concepts in solving problems involving Newton’s laws of motion In centripetal acceleration, is given by the formula a c = r ω 2 . a c = r ω 2 . Angular velocity gives the rate at which the object is turning through the curve, in units of rad/s. This acceleration acts along the radius of the curved path and is thus also referred to as a radial acceleration. An acceleration must be produced by a force. Any force or combination of forces can cause a centripetal or radial acceleration. Just a few examples are the tension in the rope on a tether ball, the force of Earth’s gravity on the Moon, friction between roller skates and a rink floor, a banked roadway’s force on a car, and forces on the tube of a spinning centrifuge. Any net force causing uniform circular motion is called a centripetal force. The direction of a centripetal force is toward the center of curvature, the same as the direction of centripetal acceleration. According to Newton’s second law of motion, net force is mass times acceleration: F net = m a . F net = m a . For uniform circular motion, the acceleration is the centripetal acceleration: . a = a c . a = a c . Thus, the magnitude of centripetal force F c F c is 6.3 You may use whichever expression for centripetal force is more convenient. Centri...

Three identical cars A,B and C are moving at the same speed on three bridges. The car A goes on a plane bridge, B on a bridge convex upward and C goes on a bridge concave upward. Let F A ​ , F B ​ and F C ​ be the normal force exerted by the cars on the bridges when they are at the middle of bridges then : Why is the following situation impossible? A mischievous child goes to an amusement park with his family. On one ride, after a severe scolding from his mother, he slips out of his seat and climbs to the top of the rides structure, which is shaped like a cone with its axis vertical and its sloped sides making an angle of θ = 2 0 . 0 0 with the horizontal as shown in above figure. This part of the structure rotates about the vertical central axis when the ride operates. The child sits on the sloped surface at a point d = 5 . 3 2 m down the sloped side from the center of the cone and pouts. The coefficient of static friction between the boy and the cone is 0 . 7 0 0. The ride operator does not notice that the child has slipped away from his seat and so continues to operate the ride. As a result, the sitting, pouting boy rotates in a circular path at a speed of 3 . 7 5 m / s. A merry-go-round is stationary. A dog is running around the merry-go-round on the ground just outside its circumference, moving with a constant angular speed of 0 . 7 5 0 r a d / s. The dog does not change his pace when he sees what he has been looking for: a bone resting on the edge of the merry-go-rou...

What is the banking of road? Banking of road: For the safety of a vehicle moving along a curved road at high speed, the road surface is kept inclined horizontally so that the outer edge of the road is at a higher level than the inner edge. This construction or arrangement of the road is called the banking of the road. The angle of banking ( θ ): The angle made by a banked road surface with horizontally is called as the angle of banking. Expression for banking of road ( θ) : 1) Consider a vehicle of mass ‘m’ moving with speed v, along a banked road. Let ‘r’ be the radius of curvature and θbe the angle of banking. 2) The forces acting on the vehicle when the vehicle is moving on a banked road are__ • The weight mg acts in a vertically downward direction. • The normal reaction N is perpendicular to the banked road. 3) The normal reaction N can be resolved into two components, • N cos θin a vertically upward direction. • N sin θalong the horizontal direction. iii) acceleration due to gravity at that place (g) Necessity banking of the road: (Need for banking of road) 1) When a vehicle moves along a horizontal curved road, necessary centripetal force is supplied by the force of friction between the wheels of the vehicle and the surface of the road. 2 Frictional force is not enough and reliable every time as it changes when the road becomes Oily or wet in the rainy season. 3) To increase the C.PE. the road should be made rough. But it will cause wear and tear on the tires of the ...