(d) State the effect on the magnitude of the centripetal force in the following cases:

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1 YEAR 12 PHYSICS: UNIFORM CIRCULAR MOTION ASSIGNMENT NAME: QUESTION 1 (a) A car of mass 1200 kg rounds a bend of radius 50m at a speed of 20ms -1. What centripetal acceleration does it experience? (b) Calculate the magnitude of the centripetal force on the car as it rounds the bend (c) Identity the type of force which supplies the centripetal acceleration in this example (d) State the effect on the magnitude of the centripetal force in the following cases: Use proportionalities in your answers (i) The radius of the bend was halved (ii) The car was moving at double its initial speed (iii) The car was twice as massive

2 QUESTION 2 (a) An electron of a hydrogen atom orbits a single proton in the centre of the atom with a radius of 5.29 x m and a speed of 2.20 x 10 6 ms -1 (a) Calculate the period of rotation (T) of the electron (b) The electron has a mass of 9.11 x kg. What centripetal acceleration does it experience? (c) Calculate the magnitude of the centripetal force which influences this circular orbit (d) Identity the type of force which supplies the centripetal acceleration in this example

3 QUESTION 3 Ganymede is a moon of the planet Jupiter and is the largest moon in our solar system. It orbits Jupiter with a mean orbital radius of 1.07 x 10 9 m and an orbital period of 7.15 Earth days. (a) Determine the centripetal velocity of Ganymede as it orbits Jupiter (3 marks) (b) Determine the magnitude of centripetal acceleration Ganymede experiences (c) Ganymede experiences a centripetal force of 1.64 x N. Determine the mass of Ganymede (d) Identify the force supplying the centripetal acceleration of Ganymede as it orbits Jupiter (e) Explain why Ganymede can be travelling at a constant speed, yet still be considered to be accelerating

4 QUESTION 4 In a student experiment, a rubber stopper of mass 20 g is swung around in a circular path above the students head. The student rotates the rubber stopper at a constant speed. The student keeps the radius constant throughout the experiment, but varies the amount of slotted masses (each has a mass of 50 g) which are suspended vertically from the apparatus (see diagram below). By adding different masses to the slotted hook, the student then needs to rotate the rubber stopper at different speeds. (a) Identify the force causing the centripetal acceleration in this experiment (b) The student records the following values for the slotted masses and the corresponding periods of rotation. (Use g = 9.81 m.s -2 ) Mass, M (kg) Force of gravity (N) Period, T (s) T 2 (s -2 ) 1 Complete the F gravity and 2 rows in the table shown above. T

5 1 (c) Use the graph grid on the next page to plot a graph of on the y axis against force of gravity 2 T (Fg) on the x axis. Make sure that you draw a line of best fit. (6) (3 marks) 1 (d) Use your graph to write down the relationship (with reasons) that exists between Fg and 2. T (3 marks)

6 QUESTION 5 A child is spun around on a merry-go-round for a period of 25 seconds. During this time, the child completes a total of 15 revolutions. (a) Calculate the average period of rotation (T) for the child (b) The diameter of the merry-go-round is 5.40 m. Determine the centripetal acceleration of the child (4 marks) (c) Using a simple vector diagram (and a little description), show that the change in velocity and hence the acceleration of the child in uniform circular motion is towards the centre of the circle. [The circle drawn below can represent the path of the object if you wish to use it.] (4 marks)

7 QUESTION 6 Two cars, labelled A and B, with masses m A = 1000kg and m B = 2000kg, move around a bend at the same speed. Find the following ratios. Explain your answers. (a) The centripetal acceleration of A : the centripetal acceleration of B. (b) The force on A : the force on B. (c) Imagine now that the two cars are driving around a race track and they both round a bend in a circular path. (i) State which car requires the greater frictional force to round the bend if they both move at the same speed with the same radius. Briefly explain your answer. (ii) State whether more or less friction would be needed to round the bend at a greater velocity

8 QUESTION 7 A toy train has a mass of 0.90 kg and is moving around a circular track of radius 2.5 m with a constant speed of 0.50 ms -1. (a) Explain what is meant by the term uniform circular motion as it relates to the toy train (b) Calculate the centripetal acceleration of the toy train (c) Calculate the magnitude of the force causing the centripetal acceleration of the train (d) State the effect on the magnitude of this force if: (i) The radius of its path was halved (ii) The train was moving 3 times faster

9 QUESTION 8 Police recently arrested a man who was walking down Hindley Street swinging an ash tray he had placed inside a nylon stocking. The ash tray had a mass of 0.75 kg and was whirled in a horizontal circle of radius 0.65 m with a constant speed. The tension in the stocking was is 125 N. (a) Find the acceleration of the ash tray. (b) Find the speed of the ash tray. (c) Find the period of the motion of the ash tray. (d) Find the number of revolutions that the ash tray made in one minute.

10 QUESTION 9 To reduce the reliance on friction, some race tracks and roads have curves which are banked at an angle. (a) On the diagram below, draw and label the forces acting on the car, of mass m, as it travels around a banked curve of radius r without relying on friction. (3 marks) (b) Explain why roads are often banked on curves. (c) A car is to travel around a bend of radius r metres at a speed of v ms -1. Show a derivation (using the forces acting on the car) which explains why the car can go around the bend with no reliance on frictional force between the tyres and the track if the track is banked at an angle θ, where tanθ = v2 rg (5 marks)

11 QUESTION 10 A car of mass 1100 kg goes around a banked track of radius 600 m at a constant speed of 60 ms -1. (a) What is the banking angle if the car negotiates the bend with no reliance on friction? (3 marks) (b) What is the magnitude of the centripetal acceleration of the car as it goes around the bend? QUESTION 11 A car moves around a banked track with a banking angle of 14. This angle is optimal for a car travelling with a speed of 50 ms -1. The normal force on the car is 20,000N. (1) Find the horizontal and vertical components of the normal force. (4 marks) (2) What is the gravitational force on the car?

12 (3) What is the mass of the car? (4) State the magnitude of the force which causes the centripetal acceleration of the car and provide a reason for your answer? (5) What is the centripetal acceleration of the car? (6) What is the radius of the bend? QUESTION 12 At one end of a racing track the radius of the bend is 300 m and the banking angle is 25. Find the speed v at which are car must travel around this bend so that there is no reliance on frictional force to provide the centripetal acceleration. (3 marks)