Solving Statics HW Problem: Piston Velocity & Acceleration

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In summary, the problem presents a diagram of a simple reciprocating engine and asks for the determination of piston velocity and acceleration at point D as functions of crankshaft angle. The dimensions and rotation rate are given and the results must be plotted. A hint is given to call AD "x" and solve in terms of known sides and angle. Two potential methods for solving are suggested.
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usher112
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Homework Statement



Using the diagram shown below for a simple reciprocating engine, determine (a) the piston velocity (velocity at point D) and (b) the piston acceleration (acceleration at point D) as functions of the crankshaft angle, θ. The dimensions are as follows: LAB=1.875”, LBD=6.0”, and ωAB=8000rpm. (c) Plot your results: VD vs. θ and AD vs. θ.



Homework Equations





The Attempt at a Solution



I don't know where to start
 

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  • #2
Hmmm, you want help on an extra credit problem that you "don't know where to start" so you can hand it in for extra credit. What's wrong with this picture? Under those circumstances I will give you only one small hint, which is probably more than I should do:

Call AD "x" and write x in terms of the known sides and angle. And use letters instead of numbers until the end.
 
  • #3

FAQ: Solving Statics HW Problem: Piston Velocity & Acceleration

What is the definition of statics in physics?

Statics is a branch of physics that deals with the analysis of objects at rest or in equilibrium. It involves studying the forces acting on an object and how they balance out to keep the object in a state of rest.

How do you calculate the velocity of a piston in a statics problem?

The velocity of a piston can be calculated using the equation v = dx/dt, where v is the velocity, dx is the change in displacement, and dt is the change in time. In a statics problem, the velocity will be zero since the piston is not moving.

What is the difference between velocity and acceleration?

Velocity is the rate of change of displacement over time, while acceleration is the rate of change of velocity over time. In other words, velocity describes how fast an object is moving, whereas acceleration describes how quickly the object's velocity is changing.

How do you determine the acceleration of a piston in a statics problem?

The acceleration of a piston can be calculated using the equation a = dv/dt, where a is the acceleration, dv is the change in velocity, and dt is the change in time. In a statics problem, the acceleration will also be zero since the piston is not moving.

Can you explain the concept of equilibrium in a statics problem?

Equilibrium in a statics problem means that the forces acting on an object are balanced, resulting in zero net force and zero acceleration. This can be achieved through the equal and opposite forces acting on the object, ensuring that it remains at rest or in a state of constant velocity.

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