Q. 313.8( 20 Votes )

A cyclist is ridi

Answer :

Now suppose the Particle is moving along x axis in positive x direction now its speed is reducing i.e. its de-acceleration or the direction of tangential acceleration (acceleration due to increase or decrease in speed) is towards negative x axis , there is another component of acceleration radial acceleration because direction of particle is also changing as it is following a circular path now direction of radial acceleration is perpendicular to the velocity of particle i.e. along Y axis


As shown in figure



Since the speed is decreasing by 0.5 m/s every second, the rate of change of speed is the tangential acceleration so the tangential acceleration is


at = -0.5 ms-2 i.e. 0.5 ms-2 opposite to the speed of cyclist along negative X axis


now radial acceleration of a particle undergoing circular motion is given by


ar = v2/r


where v is the magnitude of velocity or the speed of the particle,


r is the radius of the circular patch


now at the beginning of path speed of the particle is


v = 27 km/h


converting it to m/s


1 Km = 1000m and 1 hour = 60 × 60 = 3600 s


So v= 27 × 1000m/3600s = 27 × 5/18 = 7.5 m/s


Radius of the circular path


r = 80 m


so the radial acceleration is


ar= 0.70 ms-2 radially inwards i.e. perpendicular to velocity of cyclist along positive y axis


so the magnitude of resultant acceleration or net acceleration of the cyclist is given by


i.e.


a = 0.86 ms-2


i.e. the net acceleration of the cyclist is 0.86 ms-2 the direction is as shown in the figure above now let us find the angle made by the net acceleration of particle with radial acceleration 𝜽 which is given as


Where ar is the magnitude of radial acceleration


here ar = 0.7 ms-2


and at is the magnitude of tangential acceleration


here at = 0.5 ms-2


so we get


i.e. the total acceleration of cyclist is making an angle of 54.5o with the tangential acceleration of cyclist

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