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

In summary, the conversation involves a question about determining the velocity and angular velocity of a slider crank mechanism with specific measurements and angles. Urgent help is requested for an upcoming exam and a diagram is provided. The conversation also includes instructions for finding the equation and using the chain rule to solve for the angular velocity.
  • #1
bobmarly12345
27
0

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!
 
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  • #2
hi bobmarly12345 :smile:

can you provide a diagram? :confused:
 
  • #3
here is the photo of the diagram
 

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  • #4
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 :smile:
 
  • #5


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
 

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

1. What is a slider crank mechanism?

A slider crank mechanism is a mechanical system that consists of a slider, a crank, and a connecting rod. The slider moves back and forth in a straight line, while the crank rotates in a circular motion. The connecting rod connects the slider and the crank, allowing the linear motion of the slider to be converted into rotational motion of the crank.

2. How does a slider crank mechanism work?

The slider crank mechanism works by converting linear motion to rotational motion. As the slider moves back and forth, it causes the connecting rod to pivot, which in turn rotates the crank. This rotational motion can then be used to power other parts of the mechanical system.

3. How do you calculate the velocity of a slider crank mechanism?

The velocity of a slider crank mechanism can be calculated using the formula v = ω × r, where v is the velocity, ω is the angular velocity in radians per second, and r is the distance between the slider and the center of rotation of the crank. The angular velocity can be calculated using the formula ω = θ/t, where θ is the angle of rotation and t is the time taken for that rotation to occur.

4. How do you find the angular velocity of a slider crank mechanism?

The angular velocity of a slider crank mechanism can be found by dividing the change in angular position (in radians) by the time taken for that change to occur. This can be represented by the formula ω = Δθ/Δt. Alternatively, the angular velocity can also be calculated using the formula ω = 2πf, where f is the frequency of rotation in cycles per second.

5. What factors affect the velocity and angular velocity of a slider crank mechanism?

The velocity and angular velocity of a slider crank mechanism can be affected by various factors such as the length of the connecting rod, the size of the crank and slider, and the speed and direction of the input motion. The force and friction applied to the system can also affect the velocity and angular velocity. Additionally, the angle at which the crank is positioned can also impact the velocity and angular velocity.

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