Slider crank mechanism. Help needed to find the velocity & angular velocity.

[bobmarly12345]

Homework Statement

The instantaneous configuration of a slider crank mechanism has a crank GH 10cm long, the connecting rod HP is 50cm. The crank makes an angle of 60 degree with the inner dead centre position and is rotating at 110 rev/min. Determine the velocity of the piston P and the angular velocity of the link HP.

urgent help is needed! i have an exam soon & i have no example of this type of question to work from. please help!

 

[tiny-tim]

hi bobmarly12345

can you provide a diagram?

 

[bobmarly12345]

here is the photo of the diagram

 

[tiny-tim]

ah!

ok, call the G angle θ, and the P angle ψ (so dθ/dt = ω),

find the equation relating θ and ψ,

then use the chain rule to find dψ/dt ​

 

[DeeNos]

I understand your urgency in finding the velocity and angular velocity of the slider crank mechanism. This type of question is commonly seen in engineering and physics exams, and I will do my best to guide you through the solution process.

First, we need to understand the components and motion of the slider crank mechanism. The crank GH is the rotating part of the mechanism, while the connecting rod HP is the link that connects the crank to the piston P. The crank is rotating at a constant angular velocity of 110 rev/min, which means it completes 110 revolutions in one minute.

To find the velocity of the piston P, we need to use the concept of instantaneous velocity. This is the velocity of an object at a specific moment in time. In this case, we want to find the velocity of the piston P when the crank makes an angle of 60 degrees with the inner dead centre position. To do this, we can use the formula:

Velocity = Angular velocity x Radius

The radius in this case is the length of the connecting rod HP, which is 50cm or 0.5m. The angular velocity is given as 110 rev/min, but we need to convert it to radians per second (rad/s) to match the units of the radius. To do this, we can use the conversion factor 1 rev = 2π rad. Therefore, the angular velocity in rad/s is:

(110 rev/min) x (2π rad/1 rev) = 220π rad/s

Now, we can plug in these values into the formula:

Velocity = (220π rad/s) x (0.5m) = 110π m/s

Therefore, the velocity of the piston P at the given instant is 110π m/s.

To find the angular velocity of the link HP, we can use the formula:

Angular velocity = (Velocity of P)/(Length of HP)

We have already found the velocity of P to be 110π m/s. The length of the connecting rod HP is given as 50cm or 0.5m. Plugging in these values, we get:

Angular velocity = (110π m/s)/(0.5m) = 220π rad/s

Therefore, the angular velocity of the link HP is 220π rad/s.

I hope this explanation helps you understand the concept and solve similar problems in your exam. Remember to always pay attention to units and use the appropriate