Mechanics Revision

HCI P2 Q1

1 (a) Define upthrust.

(b) An object of mass m and density D is surrounded by air of density d. Show that the resultant force F acting downward on the object is given by

(c) A chemist uses a balance to weigh a sample as shown in Fig 1.1.

The chemist ignores the effect of upthrust and records the mass of the sample as 0.17851 kg. The density of the sample is 940.0 kg m-3 and the density of the standard mass is 8493 kg m-3 and the density of air is 1.290 kg m-3.

(i) With the help of the expression given in (b), calculate the actual mass of the sample.

(ii) Calculate the percentage error in the recorded mass. Mechanics Revision

NJC P2 Q4

4 (a) At sea level, the atmospheric pressure is 101 kPa and the density of air is 1.3 kg m-3. Calculate the height of the atmosphere if the air density remains constant throughout. You may assume that the gravitational field strength remains constant throughout.

(b) A block of wood floats in freshwater with two-thirds of its volume submerged. In oil, the block floats with 0.90 of its volume submerged. If the density of fresh water is 1000 kg m-3, find the density of oil. Mechanics Revision

(c) A non-uniform bar is suspended at rest in a horizontal position by two cords of negligible mass which make angles of 36.9° and 53.1° with the vertical as shown below. If the length L of the bar is 6.10 m,

(i) Show that T1 = 1.33 T2

(ii) Hence or otherwise, determine the distance x between the left hand end of the bar and its centre of gravity. Mechanics Revision

JJC P3 Q6

6 (a) State Newton’s Second Law of Motion

(b) A rocket is propelled by the emission of hot gases. It may be stated that both the rocket and the emitted hot gases each gain momentum. Explain how the Principle of conservation of momentum is applied in the above situation.

(c) A toy helicopter of mass 0.700 kg moves vertically upwards in still air with an acceleration of 0.500 m s-2. The effective area swept by its blades is 0.400 m2. (i) Determine the upward force on the toy helicopter by the air.

(ii) Determine the downward force on the air by the helicopter.

(iii) Calculate the speed of the air swept by the blades, relative to the helicopter. The density of the air is 1.3 kg m-3.

(iv) The toy helicopter develops a mechanical fault that causes the blades to stop rotating and it falls vertically into soft ground. Explain how the soft ground reduces the damages to the toy helicopter. Mechanics Revision

(d) A stationary submarine has a total volume of 100 m3. It is totally submerged as seen in Fig 6. The storage tank in the submarine contains 10 m3 of sea water. The density of the seawater is 1025 kg m-3.

(i) Calculate the weight of the submarine and its content.

(ii) 1. If the atmospheric pressure is 1.00 × 105 Pa and assuming that the submarine remains stationary while seawater in storage tank is being pumped out, calculate the energy required to empty the storage tank using compressed air when the water outlet is 20 m below the surface.

2. Calculate the initial upward acceleration of the submarine when the storage tank is empty.

(iii) Explain why in reality the submarine will move upwards when the water is being pumped out. Mechanics Revision

SAJC P2 Q2

2 The rocket engines of the space shuttle can exert a force of 28.6 MN at lift off when the total mass is 2.0 × 106 kg. (a) Determine the acceleration of the rocket on vertical lift-off.

(b) A 65 kg astronaut is standing on a weighing scale in the space shuttle during lift-off. Determine the reading of the scale.

(c) The rocket engine ejects 1/120 of its mass per second on lift off. Determine the speed of the ejected gas relative to the rocket engine. Mechanics Revision

(d) Some space probes use the gravitational slingshot effect to gain extra kinetic energy by swinging around an approaching planet. A simplified view of the gravitational slingshot is shown below where a space- probe of a speed of v approaches a planet of speed U in the opposite direction.

By treating this close encounter as an elastic collision, write an expression for the final speed of the space probe in terms of v and U. You may assume that the velocity of the planet does not change throughout the whole interaction.