Question

1 In many fluids, the flow velocity is observed to vary linearly from zero at the bottom to u at the top. Moreover, the magnitude F of the force acting on the top plate is found to be proportional to the speed and the area A of eaclh plate, and inversely proportional to their distance separation y The proportionality factor μ is the viscosity of the fluid. Using the above equation find out the dimensions of (10 pts.) A car travelled 120 towards the east in 10 seconds then 180 m to the west in 12 seconds and finally 240 m to the west in 15 seconds. What is the total displacement of the car (both magnitude and direction)? What is the total distance travelled? Calculate the average velocity and average speed of the car (10 pts.) 2. 3. Consider a steel ball that falls under the force of gravity (the acceleration due to gravity is g-9.8 m/s in vacuum (no air resistance force). If at time t-os, the initial position of the ball is z→200 m (z is the vertical axis), at what position will one find it at times t-2 s and t-4 s? (10 pts.) 4. A particle P travels along a straight line so that it's distance s m, from a fixed point O on the line is given by s 3t where t is the time in seconds after passing O (i) Find the velocity and speed of the particle P after 4 seconds. i) Find out the distance of turning points from the point O ii) Find the acceleration after 3 seconds. (iv) Calculate the total distance traveled during first 5 seconds. (10 pts.) 5. Two forces F 2i+3j-4 k N and F22j +6 k N are acting on a particle simultaneously. Find out the resultant force. Calculate the work done if the displacement of the particle be d-3i+2j-k m. (10 pts.) Extra credit (10 points) 6. A-2i+3j B-3i-2 j; Calculate A. B and AXB.Find out the angle between A & B

Answer 1

F = mu A u/y MLT^-2 = (mu) L^2 times LT^-1/L mu = MLT^-2 times L/L^2 times LT^-1 mu = M^1 L^-1 T^-1 The Dimensions of mu are 1, -1, -1 a) Displacement R^vector = A^vector + B^vector + C^vector = 120i^^-180i^^- 240i^^ R^vector = -300i^^ Magnitude = 300m direction - west b) Average velocity = displacement/time = -300/10 + 12 + 15 V_avg^vector = -8.11 m/s c) Average speed = distance/time = 120 + 180 + 240/10 + 12 + 15 v_avg = 14.6 m/s