Mechanical Engineering Answers

Use Hamilton's principle to show that the equation of motion for axial vibration of a tapered rod is

 Hamilton's principle to show that the equations of motion of a deep uniform beam element are

Use rules of inference to show that the hypotheses “If the weather is not too hot or not too cold, then the game will be held and a prize-giving ceremony will occur,” “If the game is held then the VC will give a speech,” “The VC did not give a speech,”  imply the conclusion “The weather was too hot.”

A woman sitting in a stationary car notices a man cycling past her at 40 km/hr. Five

seconds after he passes her car, she starts following after him. What is the shortest

possible distance in which she will catch up to the cyclist if he maintains speed and

she obeys the speed limit of 70 km/hr? The car has a maximum acceleration of 3.5m.s2

A 14 m long truck is driven alongside a 500 m long train with the same velocity of

25 m/s. The front of the truck is 7 m behind the rear of the train. At a certain instant, the

truck stars accelerating at 0,08 m/s2, while the train starts decelerating at 0,4 m/s2. How

long will it take before the rear of the truck passes the front of the train and what distance

would the truck have covered in this time?

A car of length 5 m is being driven parallel alongside a 100 m long train at the same

speed. The front of the car is 10 m behind the rear of the train. At the instant the train

decelerates at 0.4 ms² the car accelerates at 0,15 ms². How long will it take for the rear

of the car to pass the front of the train?

Water drips from a tap at uniform rate onto the floor which is 1.5m below. The first drop strikes the floor at the instant the fourth drop is on the verge of falling from the tap. What would be the location of the different drops when the first drop hits the floor? D1 is on the floor and D4 is at the tap.

During a test, a rocket travel upwards at 75m/s. when it is 40m from the ground, the engine fails. Determine the maximum height sB reached by the rocket and its speed just before it hits the ground. While in motion the rocket is subjected to a constant downward acceleration of 9.81m.s2 due to gravity. Neglect the effect of air resistance.

An elevator whose floor to ceiling height is 2.75m starts ascending with a constant upward acceleration of 1.2 m/s2. Two seconds after the start, a loose bolt drops from the ceiling towards the floor of the elevator. Calculate:

a)The time taken by the bolt to reach the floor

b)Displacement of the bolt during that time

c)The distance travelled by the bolt during the same time

A 3-phase, 4 pair of poles, 400kW, 400V, 60Hz induction motor is 780 rpm full-load speed.

Determine the frequency of the rotor current under full load condition