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1 5.8 Tutorial Topic 5 1. A car of mass 900 kg turns into a corner with a tangential velocity of 25 m s -1 – the corner has a radius of 100m. Calculate the force of friction between the tyres of the car and the road surface. 2. An object of mass 5 kg is moving in a circle with a radius 5 m at a tangential velocity of 5 m s-1 calculate the following: (a) The centripetal force required to maintain this object in this circular path. (b) The centripetal acceleration experienced by the object as it rotates in this circular path. 3. If a person is spinning around with a heavy ball in their arms - the ball moves in a circular path with radius 1.1m. The tangential velocity of the ball is 1.5 m s -1 and the ball has a mass of 3 kg. Given all this information calculate the magnitude and direction of the tension in the person’s arms. 4. The radius of the Earth is 6380 km calculate the tangential velocity of a person standing at the equator caused by the Earth’s rotation. Calculate the centripetal acceleration of this person and express it as a fraction of the acceleration due to gravity “g” – speculate on the danger of a person being thrown off the Earth’s surface. 2 5. Neutron stars are the remains of supernovae; they are tiny – just a few km across – and spin with an extremely large angular velocity. Suppose there is a neutron star of radius 20 km spins with a period of 1.2 seconds. If an object is placed at the equator of this star calculate the centripetal acceleration of this object and express it as a multiple of the acceleration due to gravity on Earth – that is multiples of “g”. 6. A large box is 4.2 m tall and 2.0 m wide with a coefficient of friction from box-to-floor of 0.60. Calculate the maximum distance, from the floor, that a horizontal force must be placed to slide the box without it rotating in the direction of motion. 7. A cylindrical grinding wheel has a radius of 30 cm, a thickness of 8.0 cm and mass of 20 kg determine its moment of inertia. 8. A solid disc has a mass of 100 kg and a radius of 80 cm. The disc rotates around an axis through its centre with an angular velocity of 9 rad s-1 determine its Kinetic Energy. 9. A 30 cm ruler rotates in a circle with the axis at one end. The ruler has an angular velocity of 0.1 rad s-1 and mass of 100 g. An insect located on the axis moves to the other end of the ruler. Determine the angular velocity of the ruler when the insect, mass 3 g, reaches the far end of the ruler. 3 10. A playground roundabout rotates about its centre on frictionless bearings with angular velocity of 1 rad s-1; it has a moment of inertia of 150 kg m2 and a radius of 1.70 m. A person, mass 50 kg climbs on the roundabout, close to the outer edge. Using the conservation of angular momentum principle determine the new angular velocity of the roundabout and the person riding on its edge.