WJEC Physics for A2: Student Bk

19 3.1 Circular motion G C mg 40 m 100 g 50 cm Exercise 3.1 1 A 3.5" hard disk drive rotates at 7200 rpm (revolutions per minute). Calculate (a) the angular velocity of the disk, and (b) centripetal acceleration of a point on the rim. [1" = 2.54 cm] 2 (a) Calculate the centripetal acceleration of the Solar System in its orbit around the centre of the Galaxy (see Section 3.1). (b) Calculate the gravitational force exerted by the Galaxy on the Sun (mass = 2.0 × 10 30 kg ). 3 The radius of a geosynchronous orbit is 42 164 km . Use the data for the ISS (Section 3.1.3 example) to show that these two orbits are consistent with the inverse square law of gravity. 4 A car of mass 1000 kg travels at 20 m s −1 around a circular bend of radius 80 m . (a) Calculate the lateral grip exerted by the tyres. (b) The maximum grip of the tyres is 9000 N . Calculate the maximum possible cornering speed of the car. 5 The car in Q4 drives on a circular car track which is banked as shown in the diagram. (a) By resolving vertically, find an equation for C and G in terms of mg . (b) If the car drives at 15 m s −1 and the θ = 10° , calculate the value of the lateral grip, G . (c) Calculate the value of θ which would allow the car to be driven at 25 m s −1 with no lateral grip (i.e. G = 0 ). 6 A load of mass 100 g is whirled in a horizontal circle on a 50 cm long thread, of breaking tension 20 N . Calculate the maximum angular velocity. 7 The load in Q6 is whirled at is now whirled at 150 rpm and the thread makes an angle of θ to the horizontal (see diagram). Calculate θ . 8 A stone of mass 500 g is whirled in a sling in a vertical circle of radius 80 cm with a frequency of 3 Hz . With the unlikely assumption that the speed of the stone is constant, calculate the maximum and minimum values of the tension in the sling and identify the points in the circle when they occur. 9 The vertical loop in a model car set has a radius of 30 cm . A 40 g car enters the bottom of the loop with just enough speed to remain in contact with the loop at the top. Calculate: (a) The speed at the top of the loop. (b) The kinetic energy and gravitational potential energy at the top of the loop. (c) The speed with which the car enters the loop. 10 The car in Q9 is observed to slow down to rest from 5.0 m s −1 to rest over a distance of 15 m on a horizontal track. (a) Calculate the frictional force (assumed constant) on the car. (b) Use your answer to part (a) to refine your answer to Q9(c), stating your assumption.