DHS 03 Dynamics (Tutorial Solutions)

DHS Year 5 Physics H2 Topic 3: Dynamics Tutorial Suggested Answers 2024 1 For Internal Use Only lim.boonsiong@dhs.edu.sg Topic 3: Dynamics Part 1: Newton’s Laws of Motion 1. A footballer accelerates a football horizontal from rest to a speed of 10 m s –1 during the time in which his toe is in contact with the ball for 0.20 s. If the football has a mass of 0.50 kg, what average force does the footballer exert on the ball? [25 N]  10 00.50 25 N0.20 vFm am t     2. The air exerts a forward force of 10 N on the propeller of a 0.20 kg model plane. If the plane accelerates forward at 2.0 ms –2, what is the magnitude of the resistive force exerted by air on the airplane? [9.6 N]     10 0.20 2.0 10 0.40 9.6 NFm a D D      3. A 5.0 g bullet leaves the muzzle of a rifle with a speed of 320 ms –1. What net force (assumed constant) is exerted on the bullet while it is moving down the 0.82 m long barrel? [312 N]     22 22 4 2 34 The bullet has constant acceleration down the barrel due to constant net force. 2 320 0 2 0.82 6.24 10 m s 5.0 10 6.24 10 312 N a vu a S a a Fm a             4. Two blocks, X and Y, of masses 3 kg and 2 kg respectively, are accelerated along a floor by a force 20 N applied to block X, as shown in the diagram. Given that the frictional forces that the floor acts on X and Y are 6 N and 4 N respectively, (a) Draw free body diagrams showing how the forces act on X and Y. (b) Base on Newton’s second law, write three equations that govern the motion of the objects (c) What are their acceleration(s)? [ 2 ms−2] (d) What is the magnitude of the force exerted by block Y on block X? [8 N] Contact forces Two solids are actually subjected to a pressure over the area where they are in contact. It is hard to calculate the pressure distribution, so instead we replace the pressure by a statically equivalent force. If the two contacting surfaces are flat, then (1) The reaction force can be modelled as a single force, with no moment (2) The force can act anywhere within the area of contact (its actual position is determined by force and moment balance) (3) The force must be perpendicular to the two surfaces (4) The force acts to repel the two solids. X 20 N Y

DHS Year 5 Physics H2 Topic 3: Dynamics Tutorial Suggested Answers 2024 2 For Internal Use Only lim.boonsiong@dhs.edu.sg (a) (b), (c) & (d)    C C -2 C C C Isolating both I Substitute value of into (1), X & Y, 20 6 4 3 2 Isolating Y, 4 2 (3) 10 2 m s5 sol we h ati ave ng X, 20 6 3 1 (2) 43 8 (1) 14 3 42 N F a a a Fa Fa Fa a Fa       