SCIENCE APPLIED DEPARTMENT (ASD) Centre for Foundation Studies and Extension Education (FOSEE)
PPH 0075 Physics I Foundation in Engineering
Assignment 2
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Chapter 6 Question 1 a) What is Newtons law of gravity ? b) [2 marks]
Figure 6 shows three different masses placed at the vertices of a right angle triangle. Calculate the total gravitational force exerted on 20 kg mass by the other two masses. [4 marks] 20 kg
6m
50 kg
8m Figure 6
30 kg
c)
i)
Prove that the total energy (E) of a satellite with a mass m moving in uniform circular motion of orbital radius r can be written as GM E m E= 2r where ME is the mass of the earth and G is the universal gravitational constant.
By assuming the satellite is moving in uniform circular motion, find the amount of work required to place a 500 kg satellite in an orbit of 300 km height from an orbit of 200 km height, given the mass of the earth, ME, is 5.98 x 1024 kg, and the radius of the earth is RE = 6.38 x 106 m. [4 marks]
ii)
Question 2:
a) Suppose Malaysians aerospace engineer team wants to place a 1500 kg weather satellite into a circular orbit 350 km above the earth surface. The earths radius is RE = 6380 km and its mass is ME = 5.97 x 1024 kg. i) Find the speed, v, and time period, T, of the satellite. ii) How much work must be done to place this satellite in orbit? [2 marks] [3 marks]
b) i) Suppose a new planet has been found (Planet X) by astronomer, which has a radius 4.5 times of Earth, and a mass of 2 times of Earth. What is the acceleration, g due to gravity near its surface? [2 marks] ii) Johannes Kepler (1572-1630) was a German mathematician, astronomer and astrologer, and a key figure in 17th century astronomical revolution. Kepler made three major discoveries that today we call Keplers Laws of planetary orbits. State the THREE laws. [3 marks]
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Chapter 7 Question 1:
a) Two uniform wires, X and Y, are connected in the manner as shown in Figure 7a. The ratio of the diameter of X to that of Y is 3:1. The ratio of the Youngs modulus of the material of X to that of Y is 1:2. If wire X has a strain of 0.01, determine the strain of wire Y. (Hint: the tensions are the same inside both wires). [3 marks]
b)
Figure 7a Figure 7b shows five immiscible liquids which are in equilibrium in a U-tube. Liquid a has a density of 0.806 103 kgm-3, liquid b has a density of 0.879103 kgm-3, liquid c has a density of 0.925 103 kgm-3, liquid d has a density of 13.6 103 kgm-3 and liquid e has a density of 1.000 103 kgm-3. i) Find the height of y.
ii) If the whole U-tube and the liquids are moved to the Moon with lower gravitational acceleration, what will be the changes (if any) to the height, y in part (i) ? [3 marks]
Figure 7b
c) The solid lead with the density of 11.3 103 kgm-3 is being placed in mercury with the density of 13.6 103 kgm-3. Show that, 16.91 % of the overall volume of the lead will float above the surface of mercury. [4 marks]
Question 2: a) A weather balloon filled with helium gas is used to lift scientific equipment of mass 200 kg. What is the volume of helium in the balloon if it is launched near the equator? If the same balloon is used on the moon, what volume of helium is required?
[Density of air at sea level, o = 1.29 kg/m3, density of helium, He = 0.18 kg/m3, acceleration due to gravity on the moon is 1/6 that of the earth.] [5 marks] 3
b) Sketch a stress-strain diagram for a copper wire and show the following: i) ii) iii) iv) Elastic region. Proportional region. Elastic limit. Breaking point.
Chapter8 Question 1 A 3.0 kg frictionless block is attached to an ideal spring force of constant 300 Nm-1. The block is then set into oscillation with an amplitude of 30.0 cm, and in such a way that the mass passes through the equilibrium point (xo) on its way towards negative displacement at time t = 0 s. For this blocks oscillation, t=0s v -1 k = 300 Nm
3.0 kg -30.0 cm a) b) c) d) e) xo = 0 cm Figure 8 30.0 cm [1.0 mark] [1.0 mark] [2.0 marks]
find the angular frequency of the oscillation, calculate the time period, determine the phase constant,
identify the equation that describes this oscillation as a function of time, and [1.0 mark] calculate the time needed for the block to go from x = 0 cm right up to the x = +25.0 cm. [5.0 marks]
Question 2: a) Find the period of a simple pendulum 75 cm long i) when it is in a freely falling elevator,
ii) when it is in a elevator moving downwards with an acceleration of 5 ms-2, iii) when it is in a train moving with a constant velocity of 20 ms-1 eastwards.
[2 marks] [2 marks] [1 marks]
b) The bob of a pendulum of length L is released from a small angle o with respect to the vertical and it undergoes simple harmonic motion given by = o cos( t + ) . 4
i) Verify that this motion is simple harmonic. ii) Find an expression for the maximum speed of the pendulum.
[3 marks] [2 marks]
Chapter 9 Question 1:
a) A uniform rod with initial length of 35 cm and diameter 2.0 cm is properly insulated, as shown in Figure 9a. The initial temperature of the rod is 20oC. When steady condition is achieved, the temperature at point X on the rod is 40oC. The amount of heat which has flown steadily through the rod in 2 minutes is 1.13 kJ. Determine the i) temperature T at one end of the rod ii) the thermal conductivity of the material of the rod iii) extension of the rod if after a few minutes the whole rod achieved the same temperature as part (i) and given the coefficient of linear expansion of the rod is 24 10-6 oC-1. [5 marks]
Figure 9a
b) A cylinder contains a helium gas of volume 8.0 10-2 m3 at pressure 150 kPa and temperature of 450 K which is represented by the initial condition of the gas, point A, as shown in Figure 9b. Curve A-B is an isothermal change while curve B-C is an adiabatic change. The gas undergoes one complete cycle ABCA. Determine the i) number of moles of helium gas, n ii) volume of helium gas, VC, if the work done on gas to move from point C to A is -3750 J iii) temperature of helium gas at point C iv) change of internal energy from point B to C if CV for helium is 12.47 J/molK v) change of internal energy for the entire cycle ABCA. [5 marks]
Figure 9b
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Question 2: a) Sketch PV diagram for the following stages of thermodynamic processes (sketch on the same PV diagram for all processes listed in i) until iv) below).
i) An ideal gas is expanded from 0.1 m3 to 0.3 m3 at a constant pressure of 3.0 atm. [1 marks] ii) The gas is then cooled at constant volume until the pressure falls to 2.0 atm. [1 marks] iii) The gas is then compressed at a constant pressure of 2.0 atm from a volume of 0.3 m3 to 0.1 m3. [1 marks] iv) The gas is heated until its pressure increases from 2.0 atm to 3.0 atm at constant volume. [1 marks] v) Find the net work done during the complete cycle [Given 1 atm = 101325 Nm-2]. [2 marks] b) A water heater is operated by solar power. If the solar collector has an area of 6.0 m2 and the intensity delivered by the sunlight (Isun) is 550 Wm-2, how long does it take to increase the temperature of 1.0 m3 of water from 20.0 oC to 100 oC ? [Given that density of water, w = 1000 kgm-3 and specific heat of water, cw = 4.19x103 Jkg-1oC-1] [4 marks]
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