Answered You can hire a professional tutor to get the answer.
1 Define the common derived units of the following physical quantities; and express them in terms of the base units: Mass, Length, Time and Electric...
A large caravan of mass 1100 kg is being towed by a large family saloon car of mass 1400kg. To join smoothly to the motorway, the driver believes he needs to speed up with an acceleration of 2m/s2. The drag forces on the caravan and the car are 400 and 200 respectively. If the engine provides 8kN of motive force and assuming that the drag forces remain constant,i) Calculate the acceleration which can be achieved. Will the drive gets the acceleration he needs?ii) Calculate the force that the car exerts on the caravan at the acceleration you have obtainedForce, Velocity, Acceleration, Energy, Density, Pressure, Power, Momentum, Speed Mass (m): Is the amount of matter that a body contains, and a measure of the inertial property of the body, that is, of its resistance to change of motion (inertia). Is expressed by Kg. Length (d or S): is a measurement of distance or dimension. Is expressed by (m). Time (t): Are the quantities or measures the interval between events, or the duration of events. Is expressed by (S). Electric charge (Ec): Is a fundamental property of some subatomic particles, which determines their electromagnetic interactions. Is expressed by (J) Force (F): is a net force acting on a body courses that body to accelerate; that is; to change its velocity. Is expressed by ( N, Nm or Kgm/s^2) Velocity (V or U): is a vector measurement of the rate and direction of motion. Is expressed by (m/s) Acceleration (a): is defined as the rate of change (or time derivative) of velocity. Is expressed by (m/s^2) Energy (…): is the property (or the quantity of the property) of changing the state of a system or doing work. Is expressed by (J) Density (….): is a measure of mass per unit of volume. Is expressed by (Kg/cm^3) 10) Pressure: is the measure of the force the acts on unit area. Is expressed by (…) 11) Momentum: is a physical quantity related to the velocity and mass of an object or is the product of the mass and velocity of an object. Is expressed by (Kgm/s) 12) Speed(S): is the rate of motion, or equivalentently the rate of change of position, expressed as distance d moved per unit of time t (m/s) Q 1.2. Use the method of dimensions to verify the following formulae: P = mv P= Kg*m/s , so P is expressed by Kgm/s EK = ½ mv2 Ek= Kg*(m/v)^2, so we know (a/b)^2 is equal to a^2/b^2 , so Ek= Kg*m^2/s^2. In fact Newton is equal to Kgm/s^2 => Ek= kgm/s^2*m =>Ek= Nm. So we know Nm is equal to joule that maens Ek= Nm or J Ep = mgh Ep= kg*m/s^2*m, so we know kgm/s^2 is equal to N. That means Ep= Nm. In fact Nm is equal to Joule, so Ep could be expressed by Nm or J v2 = u2 + 2as. V^2= (m/s)^2 + m/s^2*m, => V^2= (m/s)^2 + m^2/s^2 because a*a=a^2 We know if you have a^2/b^2= (a/b)^2, so we have V^2= (m/s)^2 + (m/s)^2,=> V^2= 2(m/s)^2. In mathematics if you have a^2=b^2 is equal a=b, so V is expressed by m/s S = ut + ½ at2 S= m/s*s+ m/s^2*s^2, we simplify s^2 by s^2 and s by s, we have S= m+m is equal to 2m. So S is expressed by m(meter) P = w/t Work done is expressed by Joule and W= F*l => W= m*a*l ( F=m*a), so P=m*a*l/t => P= (kg*m/s^2*m)/s (Kgm/s^2= N), so P= Nm/s or J/s F = ma F= Kg*m/s^2, we know kgm/s^2 is equal to Newton, so F is expressed by Newton ( F= N) t = t’/√(1 – (v2/c2)) t^2= t’^2(- v^2/c^2), t^2= s^2 Q2.1 a) Using the information provided in the appendix, calculate the amount of time required for an electromagnetic signal sent by the astronauts landed on the surface of the Moon to reach the control base on Earth. Formula We know d= v*t, so t = d/v Speed= 310^8 m/s Solution b) A car is being driven along a straight and level road at a steady speed of 25 ms-1 when the driver suddenly notices that there is a fallen tree blocking the road 65 meters ahead. The driver immediately applies the brakes giving the car ````a constant retardation of 5 ms-2. How far in front of the tree does the car come to a halt? Formula v^2= u^2 + 2as, so S= (v^2-u^2)/2a Solution S= (0^2 – 25^2)/2*(-5) S= 62.5 mSo we can take away the 62.5 meters traveled while decelerating, from the 65 meters from where the tree was spotted.So S=65-62.5 = 2.5 meters that the car came to a halt in front of the tree. If the driver had not reacted immediately and the brakes were applied one second later, with what speed would the car have hit the tree? formula v^2 = u^2+ 2as a=-5 m/s2 s= 65-25= 40msolutionv^2 = 25^2 + (-5)*40v^2 =225 v =15^2*1/2 v = 15 m/sso, the car hit the tree with a velocity of 15 m/s c) The table below shows the velocity of a car on a journey. t/s 0 10 20 30 40 50 60 70 80 82 84v/ms-1 0 15 30 45 60 60 60 30 0 8 0Draw a v-t diagram (preferably on a graph paper) for the car’s journey; Explain the journey of the car up to the 80th second; Calculate the acceleration of the car during the first 40 second of its journey; Calculate the distance it has traveled during the first 80 second of its journey; Calculate the acceleration of the car during the last 20 second of its journey; What do you think it has happened to the car between the 80th and the 84th seconds. d) A stone is thrown upward with a velocity of 20m/s. Calculate: i) How long does it take for the stone to reach its highest point; ii) the maximum height it will achieve? Q2.2 a) A large caravan of mass 1100 kg is being towed by a large family saloon car of mass 1400kg. To join smoothly to the motorway, the driver believes he needs to speed up with an acceleration of 2m/s2. The drag forces on the caravan and the car are 400 and 200 respectively. If the engine provides 8kN of motive force and assuming that the drag forces remain constant, Calculate the acceleration which can be achieved. Will the drive gets the acceleration he needs? Calculate the force that the car exerts on the caravan at the acceleration you have obtained. b) In a test to find a lorry’s stopping brakes a lorry of mass 2.5 tones is driven at a velocity of 15m/s. At a certain moment he driver make an emergency stop. If it Q2.3. Define Kinetic and Potential Energies (Ek, Ep), write their formulae and explain the variables and their units. Provide an example of a device in which there is continuous exchange of Ek and Ep . Q2.2. A ball bearing of mass 250g is released from the top edge into a glass ball. The height of release is 10cm. become maximum, providing a reason for your choice. b) Calculate the maximum speed of the ball when oscillating inside the ball. The ball bearing is now changed to one with mass of 100g. What difference would you expect to observe in the maximum speed of the ball bearing? Provide a reason to support your answer. Q2.3. A man of mass 75 kg is running up a staircase in 5 seconds. The oblique length of the staircase is 13m. If the bottom of the staircase is 5m away from the wall, Calculate the man’s total Gravitational Potential Energy (GPE) gain. Calculate the man’s power. Q2.4 A ball of mass 350g is travelling with a speed of 4m/s when it hits at right angles a fixed vertical wall. The ball rebounds with a speed of 3m/s. Find the magnitude of the impulse exerted by the ball on the wall. Using a simple diagram show the direction of velocities and the impulse. Two particles P and Q of mass 2kg and 5kg respectively are moving towards each other along a straight line on a smooth horizontal surface. The particles collide. Before the collision the speeds of P and Q are 6m/s and 4m/s respectively. After the collision the direction of motion of P is reversed and its speed is 1.5m/s. Find: The speed and direction of Q after the collision. The magnitude of the impulse given by P to Q in the collision. Q3.1 A particle P is attached to one end of a light inextensible string. The other end of the string is attached to a fixed point O, on the ceiling. A horizontal force of 12 Newton is applied to the P. The particle is at equilibrium with the string taut and OP makes an angle 20ᵒ with the downward vertical. Find: The tension in the string; The mass of the particle. A particle of weight W Newtons is attached at C to the ends of two light inextensible strings AC and BC. The other ends of the strings are attached to tow fixed points A and B on a horizontal ceiling. The particle hangs in equilibrium with AC and BC inclined to the horizontal at 30ᵒ and 60ᵒ respectively. Given the tension in AC is 50N, calculate: The tension in BC to 3 significant figures, The mass of the particle. Q3.2 (a) The diagram below shows a pole vaulter holding a pole horizontally. He keeps the pole in equilibrium by exerting an upward force, U, with his leading hand and a downward force, D, with his tailing hand. For the situation shown in the figure, calculate forces U and D showing your work and providing your reasoning. Explain the effect on the magnitude of U and D if the vaulter moves his leading hand closer to the centre of gravity of the pole while pole is still in equilibrium. 3.2 ( b) The diagram shows a woman is standing on a cantilevered balcony. All the values of the forces and measurements are given in the diagram. Calculate the value of the support force S, giving the details of your work. Q3.3 Write an article of about 500 words, describing the nature of friction, viscosity and turbulence and the factors affecting them. Express any formulae involved, with their elements and units of measurement. Q3.4 Peter is pulling Paul who is on a toboggan, along a rough horizontal snow surface using a rope which makes an angle of 30ᵒ with the horizontal. Paul and the toboggan have a total mass of 40kg and the toboggan is moving with a constant speed in a straight line. Given the tension in the rope is 50N, find the coefficient of friction between the toboggan and the snow. Q3.5 Relativity: Time dilation: t’ = t/(1 – (v2/c2)) where t’ is the duration of a second recoded by the clock on the space ship and t is the duration of a second measured on Earth. Length contracts: l = l0(1 – (v2/c2)); where l is the length onboard the ship and l0 is its original length on Earth; and The mass Increment: m = m0 / (1 – (v2/c2)); where m is the mass of the object onboard the ship and m0 is its original mass on Earth, (the rest mass). a) Draw the time dilation factor 1/ (1 – (v2/c2)) as a function of v, for 0 ≤ v ≤ 0.99c; b) Explain what happens to the time, length and mass of an object on board a spaceship travelling with the speed of light; c) Calculate the relativistic length and mass of a meter rule on board a space ship moving with a velocity v = 0.99c. The rest mass of the ruler is 100g. d) The “Twin Paradox”: Terra and Stella are identical twins who celebrate their twentieth birthday on Earth, before Stella boards a spaceship moving with a velocity of .99c toward the Alpha Cetauri, 25 light years away. The ship reaches the Alpha Centauri and immediately turns around bringing Stella back to Earth. According to the clocks on Earth the trip takes around 50 years. How old are the twins when they meet again? Appendix: km; Speed of electromagnetic radiation in free space (& atmosphere) = 3.0x 108 m/s
