Jurong Junior College 2014 J1 H1 Physics (8866) Tutorial 3: Forces

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1 Jurong Junior College 2014 J1 H1 Physics (8866) Tutorial 3: Forces Take g = 9.81 m s -2, P atm = 1.0 x 10 5 Pa unless otherwise stated 1. Draw the free body diagram / force diagram for the following : (a) Skydiver Coin Book (c) 110 N mass man s left leg w 2 mass (d) 1.0kg mass 2.0 kg mass 3.0 kg mass (e) 5.0 kg mass 4.00 kg mass 3.00 kg mass (f) Left Box Right Box KPL/2014 Page 1 of 6

(g) 2.0 kg mass 3.0 kg mass 10.0 kg mass 2. (a) State the conditions necessary for a rigid body to be in equilibrium. [2] Fig. 2.1 shows an object M of mass 20 kg is supported by a hinged uniform rod of mass 10 kg and string.

2 (g) 2.0 kg mass 3.0 kg mass 10.0 kg mass 2. (a) State the conditions necessary for a rigid body to be in equilibrium. [2] Fig. 2.1 shows an object M of mass 20 kg is supported by a hinged uniform rod of mass 10 kg and string. wall string Fig hinge 1.5 m M = 20 kg 2.0 m (i) Two of the forces acting on the rod are shown in Fig.2.2. Sketch the remaining two forces acting on the rod by drawing & labelling them clearly on Fig.2.2. [2] A F, force on rod by wall W, weight of the rod Fig.2.2 By taking moment about hinge A, calculate (ii) the tension in the string, [2] [T = 462 N] (iii) both the horizontal component and the vertical component of the force F acting on the rod by the wall. [4] [F X = 327 N, F Y = 32.4 N] KPL/2014 Page 2 of 6

3 3. (a) A small ball of weight W is suspended by a light thread. When a strong wind blows horizontally exerting a constant force F on the ball, the thread makes an angle θ to the vertical as shown in the diagram. State an equation relating θ, F and W. θ F W (c) A body of mass 1.50 kg is placed on a plane surface inclined at 30 o to the horizontal. Calculate the friction and normal reaction forces which the forces must exert if the body is to remain at rest. [7.36 N; 12.7 N] A uniform rod XY of weight 10.0 N is freely hinged to a wall at X. It is held horizontal by a force F acting from Y at an angle of 60 o to the vertical as shown in the diagram. Find the value of F. [10 N] 4. A trailer of weight 30 kn is hitched to a cab at the point X as shown in the diagram below. If the trailer carries a weight of 20 kn at the position shown in the diagram, calculate the upward force exerted by the cab on the trailer at point X. [20 kn] 2010 / RI / H2 / P2 Q2 5 (a) A mass hanging from a spring balance in air gives a reading of 50 N. When the mass is completely immersed in water, the reading on the balance is 40 N. It is now completely immersed in another liquid, giving a reading of 34 N. Calculate the density of this liquid. Assume that the density of water is 1000 kg m -3. [1600 kg m -3 ] In Fig. 5 below, a uniform beam of length 10.0 m and weight 500 N is hinged to a wall at point O. Its far end is supported by a cable that makes an angle of 53.0 with the horizontal. A 70.0 kg worker stands on the beam. KPL/2014 Page 3 of 6

4 cable O s Fig beam (i) Draw a labelled diagram showing the forces acting on the beam. (ii) (iii) The worker walks towards the far end of the beam from O. Calculate the furthest distance s he can walk if the maximum possible tension in the cable is 1000 N. [7.99 m] Calculate the magnitude of the force exerted by the hinge on the beam when the tension in the cable is 1000 N. [716 N] 6 (a) A spring obeying Hooke s law has an unstretched length of 20 cm and a spring constant of 400 N m -1. What is the tension in the spring when its overall length is 40 cm? [80 N] Some weight-lifters use a chest expander, consisting of a strong spring with a handle at each end, to exercise chest and arm muscles. For one such chest expander obeying Hooke s law, the force F applied by the weight-lifter is proportional to the extension x of the spring. Given that the spring constant k is 400 N m -1 and assuming that the limit of proportionality is not exceeded, i) plot a graph showing how W, the work done depends on the extension x. ii) calculate the work done required to extend its length by 10 cm with a force of 40 N. [2 J] 7 Calculate the actual pressure at the bottom of an open barrel of diameter m filled with kg of water and kg of olive oil. Assume the 2 liquids are perfectly immiscible (i.e. insoluble). (Take density of water = 1000 kg m -3, density of olive oil = 920 kg m -3 ) [1.25 x 10 5 Pa] KPL/2014 Page 4 of 6

5 8. A cable car travels along a fixed support cable and is pulled along this cable by a moving draw cable. For the situation shown, where the cable car can be considered to be stationary and the draw cable exerts negligible force on it, the weight, W of the cable car and the passengers is 8.0 x 10 4 N. (a) Sketch a vector triangle to show the weight, W of the cable car and passengers and T 1 and T 2, the two cables. Find the magnitude of T 1. [136 kn] [8866 / Nov 2011 / Paper 2, Q5] 9. (a) Explain what is meant by the following terms when used in the context of forces. (i) equilibrium (ii) friction (iii) centre of gravity (iv) moment (v) torque of a couple (c) A truck of mass kg is stationary on a hill with a gradient of 15. The three forces acting on the truck are its weight, a frictional force parallel to the road and a reaction force normal to the road. (i) Draw a triangle of forces to show that the truck is in equilibrium. Label each force. [2] (ii) Determine the numerical value of each of the three forces, using the same labels as you used in (i). [3] [W = 383 kn, f = 99 kn, N = 370 kn] Friction is often regarded as a nuisance. (i) State two different situations where friction is of critical importance. [2] (ii) For one of your examples explain why friction is so important. [1] KPL/2014 Page 5 of 6

6 Optional Questions [Extra Practice] 1. A water wheel has eight buckets equally spaced around its circumference, as illustrated in the figure on the right. The distance between the centre of each bucket and the centre of the wheel is 1.6 m. When a bucket is at its highest point, the bucket is filled with a mass of 40 kg of water. The wheel rotates and the bucket is emptied at its lowest point. (a) (c) (d) Define the moment of a force. Write down the number of the bucket that provides the largest moment about the axle of the wheel. [3] Write down the numbers of those buckets containing water that cause a moment about the axle. [2, 3, 4] Calculate, for the wheel in the position shown in the figure, the total resultant moment about the centre of the wheel of the water in the buckets. [1520 N m] 2. A uniform horizontal beam of mass 30.0 kg, 5.00 m long is attached to a wall by a hinge that allows the beam to rotate. Its far end is supported by a cable that makes an angle of 53.0 o with the horizontal. Wall Rope Box Hinge 53.0 º beam 5.00 m If a box of mass 60.0 kg is placed 1.50 m away from the wall, find the tension in the cable and the force exerted by the hinge on the beam. [405 N; 610 N] KPL/2014 Page 6 of 6

Jurong Junior College 2014 J1 H1 Physics (8866) Tutorial 3: Forces (Solutions)

Jurong Junior College 2014 J1 H1 Physics (8866) Tutorial 3: Forces (Solutions) Take g = 9.81 m s -2, P atm = 1.0 x 10 5 Pa unless otherwise stated Learning Outcomes (a) Sub-Topic recall and apply Hooke