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## Homework Statement

A cylinder in a truck engine are shown in

Figure Q8.1 below. The piston slides without friction in the cylinder of diameter

150 mm. The combustion chamber is subjected to an internal pressure of

50 bar gauge as a result of fuel combustion without any leakage past the piston.

The connecting rod AB has a length of 200 mm. It is linked to the piston at A

and to the crank-shaft at B. The crank-shaft OB has a revolution radius of

75 mm

1 - Calculate the resulting instantaneous force on the piston if downward force is 80kN about the crankshaft axis of rotation O..

2 - Calculate the angle OAB.

3 - Calculate the projection of the force transmitted by the piston to connecting rod AB.

4 - Isolate crank pin OB and calculate the moment resulting from the force transmitted by connecting rod AB.

Consider an anti-clockwise rotation as positive.

5 - Calculate the rotational velocity of the engine crankshaft if engine is running at 1500rpm.

6 - What is the crankshaft power output of a 6 cylinder engine at this running

condition if the average torque produced on the crankshaft at a certain

engine load in one cylinder at 1500 rpm is 170 Nm?

## Homework Equations

## The Attempt at a Solution

Are these answers right?[/B]

1 - 50BAR = 5,000,000Pa, P=F/A so F=PA.

A = pi r^2, r= 0.075 so area = 0.01767m^2.

F=5,000,000 x 0.01767 = 88350N

2 - Length AB = 0.2m OB= 0.075m

therefore OAB= sin (0.075/0.2) = 22.02 degrees.

3 - Projection of force, 80,000 = adjacent, therefore Force on AB = 80,000/cos(22) = 86,282.8N

4 - Moment on OB from AB = 80,000 x 0.075 = 6000Nm as only vertical force of 80,000N can act on OB?

5 - Rotational velocity = 2pi x f.

1500rpm = 25Hz, therefore Rotational velocity = 2pi x 25 = 157.08 rad/s

6 - Torque = 170Nm, Power = Work/time

Work = 170 x 1500 x 6 = 1,530,000N for all 6 cylinders per minute

Power = 1,530,000/ 60 seconds = 25,500W

Thank you, I hope these are mostly right. I'm not sure about last one.

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