DHS 04 Forces (Tutorial)

DUNMAN HIGH SCHOOL 2024 Year 5 H2 PHYSICS 1 Forces Tutorial Hooke’s Law & Upthrust 1. A sealed U-tube contains nitrogen in one arm and helium at pressure P in the other arm. The gases are separated by mercury of density ρ with dimensions as shown in the diagram. The acceleration of free fall is g. What is the pressure of the nitrogen? A p B xρg C p + xρg D p + (x+y)ρg 2. A 10 kg mass is suspended from two spring scales that read in kilograms as shown, each of which has negligible weight. Which statement is correct? A The top scale will read zero, the lower scale will read 10 kg B Each scale will read 10 kg C Each scale will read 5 kg D The lower scale will read zero, the top scale will read 10 kg 3. A boat with its cargo has a total mass of 1.2 x 10 7 kg. Taking the density of water to be 1000 kg m−3, calculate (a) the upthrust on the boat when it is in stable equilibrium, [1.18 × 108 N] (b) the volume of the boat below the water line. [1.20 × 104 m3] 4. A spring A of spring constant 6.0 N m -1 is connected in series with a spring B of force constant 3.0 N m-1. One end of the combination is securely anchored and a force of 0.6 N is applied to the other end. (a) By how much does each spring extend? [0.10 m, 0.20 m]

2 (b) What is the force constant of the combination? [2.0 N m-1] 5. A light spring is attached between a 2.0 kg and 3.0 kg trolley as shown. The spring constant of the spring is 4.0 N cm-1 and it obeys Hooke’s law. A 20 N force is applied horizontally to the 2.0 kg trolley. The trolleys move on a level floor. Neglecting the effect of all resistive forces, what is the compression in the spring? A 0 cm B 3.0 cm C 5.0 cm D 6.0 cm 6. A beam, the weight of which may be neglected, is supported by three identical springs. When a weight W is hung from the middle of the beam, the extension of each spring is x. The middle spring and the weight are removed. What is the extension, in terms of x, when a weight of 2W is hung from the middle of the beam? (J03/I/22) Ans: 3x 7. A toy which has a mass of 50 g works by the use of a compressed spring. The spring is compressed by 2.0 cm when a force of 20 N is exerted on it. A child releases the toy after compressing the spring by 3.0 cm. How high above the point of release can the toy jump? [0.917 m] 3.0 k 2.0 k 20 N

3 Equilibrium of Forces and Turning Effects of Forces 8. A block is attached to a uniform beam using a light string. The beam is horizontal and in equilibrium on a pivot, as shown in Fig. 8.1. Fig.8.1 (not to scale) The weight W of the beam acts at a distance of 8.3 cm from the pivot. The weight F of the block acts at a distance of 1