H1.04. 2022 Forces Tutorial Solutions

1 Types of Forces Tutorial – Solution Q1 Ans: A Compression of air, the fall of water droplets and the spreading of petrol all have very little resistance to its motion. But when applying paint to the surface of a wall it would actually take more effort to ‘push’ the paint across the wall. Q2 (a) Friction is the force which opposes the relative motion of the two bodies in contact or tends to oppose one body from moving relative to the other. (b) (i) 1. Friction is useful in braking when the brakes of a moving car is stepped. 2. Friction is a useful force to enable walking by the floor exerting a forward force on the shoe/foot. 3. Friction provides the driving force of a car through the frictional force exerted by the road surface on the tire in the forward direction of the car. 4. In unloading heavy wooden crates from a lorry on an inclined plank, friction slows down the crates as the crates slide down the plank. (ii) Without friction during braking, the car will skid and may result in accident. Without friction between the floor and the shoe/foot, a person may slip and falls. Without friction to provide driving, it is difficult to control a vehicle on the road which will result in accident. Without friction during unloading heavy wooden crates on the incline plank, the crates may slide down too fast and cause injury to workers. 1 2 1 Q3 Ans: B For parallel combinations, keff = k1 + k2 (make sure you know how to derive this) F = keff x 10 = 2k (0.2) k = 25 Nm-1 Q4 When W = 0 N, the length L is the natural length (Lo) of the spring. From the graph, when W = 0 N, L = Lo = 6 cm Using Hooke’s Law, Fs = ke where Fs = force on spring, e = extension of spring, k = spring constant Therefore, sFk e Using the point ( 5 N, 10 cm), o Wk N mLL 1 2 5 () (10 6) 10     = 125 N m-1

2 Q5 First, find the resultant force FR of the 3 coplanar forces: y-component of the resultant force, Fy = 40 N x-component of the resultant force, Fx = 50-20 = 30 N tan θ = (30/40)  θ = 36.9° Resultant = 504030 22  N To maintain equilibrium, the counter force must be of same magnitude but in opposite direction to FR. Hence, F = 50 N at bearing of 220° (2 s.f.) 1 1 1 Q6 As this is an equilibrium system, resultant force is zero and resultant torque is zero. Hence all three lines of force must intersect at a common point, and, when the force vectors are joined head-to-tail they should form a closed triangle with arrows pointing in the same direction (anticlockwise in this case). Answer: B Q7 Essential questions 1. What is this force that the question speaks of?  force of gum on tooth 2. What does it mean that the tooth is in equilibrium?  no net force acting on body, and no net moment about ANY POINT on the tooth. 3. Given the directions of the two 2.5 N forces, which is the onl