![]() ![]() A cylinder of around 4 meters in diameter is set spinning. Since this is slightly less than the weight of the aircraft, the aircraft will lose altitude unless the lift is increased by increasing the speed or pulling the nose of the aircraft up. The lift force is always perpendicular to the wings and so the aircraft's weight has to be supported by the vertical component of the lift. To make a turn, the ailerons are operated so that the aircraft banks and the horizontal component of the lift supplies the necessary centripetal force to make the aircraft turn. A banking aircraft uses the horizontal component of the lift force to provide the centripetal force for turning.Īn aircraft in straight, level flight experiences a lift force perpendicular to the surface of its wings which balances its weight, mg. The horizontal component of the normal forces of the rails on the train provide the centripetal force. In this case, so that at a certain speed no lateral thrust has to be exerted by the outer rail on the flanges of the wheels of the train, otherwise the rails are strained. Dividing both equations, tan θ=v 2/ rgĪ bend in a railway track is also banked. Also the car is assumed to remain in the same horizontal plane therefore no horizontal acceleration therefore, N cos θ= mg. ![]() N sin θ= mv 2/ r where m and v are the mass, speed and r is the radius of the bend respectively. Treating the car as a particle and resolving N vertically and horizontally we have, since N sin θ is the centripetal force. The problem is to find the angle θ at which the bend should be banked so the centripetal force acting on the car arises entirely from a component of the normal force, N of the road. Safe cornering that does not rely on friction is achieved by banking the road. If the centripetal force is less than the force wanting to pull the car out, a skid will result. The resultant of these two forces is the centripetal force. The other more important horizontal force is the frictional force exerted inwards by the road on the tyres of the car. The direction of the force exerted by the air will more or less oppose the instantaneous direction of motion. This force arise from the interaction of the car with the air and the road. If a car is travelling round a circular bend with uniform speed on a horizontal road, the resultant force acting on it must be directed to the centre. We can also measure the force required to produce the same extension of the same using a spring balance and compare the two forces. We know the m and the radius and therefore the extension of the spring. The velocity of the turntable can be found by measuring the time it takes for the turntable make ten revolutions and dividing by ten. When the truck just hits the truck the extension of the spring is of known length. ![]() As the speed of the turntable is increased the spring extends until the truck reaches the stop at the end of the rails. Opposing the motion of the truck is a spring which provides the centripetal force required to keep the truck in position. The turntable is rotated by the electric motor causing the truck of known mass m to move out from the centre of the turntable. Experimental Measurement of Centripetal Force In all cases it is important to appreciate that the forces acting on the body must provide a resultant force of magnitude mv 2/ r toward the centre. Other examples of circular motion will be discussed in the following sections. Therefore, X'Z'=v 2/r δt.Ī=change in velocity/time interval = (v 2δt/r)/δt=v 2/r. Then the length of XZ in the figure will be almost the same as X'Y' in b) X'Z'=rδθ but also δθ=vδt/r. Since one vector (- v A) is perpendicular to OA and the other v B is perpendicular to OA and the other v B is perpendicular to OB, therefore ∠ XYZ = ∠ AOB =δθ The change in velocity between A and B obtained by subracting v A from v B.Ĭhange in velocity = v A and v B. The vectors v A and v B represent the velocities at these points. If it travels from A to B in a short interval of time δ t then, since speed = distance x time, arc AB = vδ t.Īlso by the definition of angle in radians, arc AB = r δθ= v δt. The expression for the acceleration of an object moving in circular motion of radius r moving at a constant speed v is derived as follows. ![]()
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