Engineering Mechanics Assignment 2 Due 24 October 2012 10AM Answer all Questions Total 60 Marks Question 1 (5 marks) A rectangular plate shown in vertical section AB, is 7m high and 10m wide(normal to...

Engineering Mechanics
Assignment 2 Due 24 October 2012 10AM
Answer all Questions Total 60 Marks
Question 1 (5 marks)

A rectangular plate shown in vertical section AB, is 7m high and 10m wide(normal to the plate of the paper) and blocks the end of a fresh water channel 5m deep. The plate is hinged about a horizontal axis along its upper edge through A and is restrained from opening by fixed ridge B which bears horizontally against the lower edge of the plate. Find the force B exerted on the plate by the ridge.
Question 2: (12 marks)

A TV camera following a Rugby World Club match is transported along the
sideline of the pitch on a motorised cart.
During a period of play, the position of the camera is given by
S = 0.5 t³ -10 t² + 28 t + 40 where S is measured in meters
along the sideline for a time interval of 0-15 seconds.

1. Determine a function for the velocity and acceleration of the TV camera.
2. Use Matlab to plot the displacement, velocity and acceleration of the camera for the first 15 seconds and attach plots to your assignment submitted.

1. Determine the maximum and minimum position values of the camera and the minimum velocity (Negative velocity) in the first 15 seconds, using derivatives.

(Hint: you can use functions like roots, polyval to solve these in Matlab)

1. At what time (0 -20sec) was the camera on the 50m mark.

(Hint: you can use functions like roots, polyval to solve these in Matlab)
Question 3a (10 marks)
3a) A shell is fired from a cannon with a velocity of 200m/s at angle of 30⁰ to the horizontal from the edge of a 60m high cliff. Determine

1. The maximum height to which the shell rises, and
2. How far from the bottom of the cliff is the shell when it hits the ground.

(The acceleration due to gravity is equal to 9.81 m/s²)

30⁰
60m

Question 3b (10 Marks)
A ground base launches a self-propelled rocket from a moving reference position on ground. The rocket has an acceleration of a = t +5 m/s² where t is time in seconds with reference to start time of zero seconds and initial reference position 10 m above ground and initial velocity of 2m/s upwards .

1. Determine the speed of the rocket as a function of time relative to the ground position.
2. Determine the distance travelled as a function of time relative to the ground position.
3. What is the speed and distance covered in 10 seconds after launching the rocket from the reference position.

Question 4
Use the principle of Energy Conservation to calculate the force required to accelerate a body of mass 700kg from 20m/s to 40 m/s over 250m up a gradient of 10deg to horizontal, if the traction resistance remains constant at 100N.
(7 Marks)
Question 5

5a) Passengers in a transport airplane A flying due east at a speed of 130 m/s observe a second airplane B that passes under A in horizontal flight. Although the nose of plane B is pointed in the 40⁰ northeast direction, air plane B appears to the passengers in A to be moving away from the transport in the 60⁰ northwest direction. Determine the true velocity of airplane B. Write the vector equation for the velocities and draw the vectors in terms of a vector triangle. (4 marks)

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5b) A cyclist travels at a velocity of 20 km/h in a direction north. A car approaches the cyclist from the opposite direction at a velocity of 50 km/h south. What is the velocity of the cyclist relative to the driver in the car? (2 marks)
Question 6 10 Marks

The 2000 kg pickup truck accelerates at a rate of 3m/s² from rest on a 1 in 10 incline as shown above. The centre of gravity is 600mm above the surface of the road and each wheel is positioned at 1500mm from the centre of gravity.
Calculate the normal force under each pair of wheels and the friction force under the rear driving wheels. Assume the wheels do not slip.