Minimum Force (roller over step)

In summary, the conversation is about calculating the minimum force, P, required to pull a roller over a step on an inclined plane with a radius of 0.685m and an angle of inclination of 12°. The sum of the moment forces is set to 0, which leads to the equation 0 = mg(sin(φ)*(r-h) + mg(cos(φ)*√[r2-(r-h)2] - P(cos(θ)*r-h). However, there appears to be a missing term, P sin(θ), which may have resulted in an incorrect answer. Further clarification is needed to determine the correct value of P.
  • #1
BMcC
32
0
qUgpWXX.jpg


On an inclined plane (φ = 12°), calculate the minimum force P required to pull the roller over the step. The radius of the roller, r = 0.685m

My attempt

The sum of the Moment force about the system = 0

0 = mg(sin(φ)*(r-h) + mg(cos(φ)*√[r2-(r-h)2] - P(cos(θ)*r-h)

P(cos(θ)*r-h) = mg(sin(φ)*(r-h) + mg(cos(φ)*√[r2-(r-h)2]

P(cos(32.9)*0.575m) = (26kg)(9.8)(sin(12)*(0.575) + (26)(9.8)(cos(12)*√[0.6852 - (0.575)2]

0.483*P = 30.46 + 92.79

P = 255.17



This answer appears to be wrong. Any help on this? I can't seem to figure out where I went wrong.
 
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  • #2
BMcC said:
0 = mg(sin(φ)*(r-h) + mg(cos(φ)*√[r2-(r-h)2] - P(cos(θ)*r-h)
I guess you meant ##0 = mg\sin(φ)(r-h) + mg\cos(φ)\sqrt{r^2-(r-h)^2} - P\cos(θ)(r-h)##.
What about P sin(θ)?
 

1. What is minimum force?

Minimum force is the smallest amount of force required to move an object from one position to another. In the context of a roller over step, it refers to the minimum amount of force needed to roll over a step or obstacle.

2. How is minimum force calculated?

Minimum force is typically calculated by taking into account the weight of the object, the height of the step, and the angle of the slope leading up to the step. It can also be calculated using the principles of mechanics and dynamics.

3. Why is minimum force important?

Minimum force is important because it allows us to determine the most efficient way to move an object over a step or obstacle. By minimizing the amount of force needed, we can reduce the risk of injury and save energy.

4. How can minimum force be reduced?

There are several ways to reduce minimum force, including increasing the angle of the slope leading up to the step, decreasing the weight of the object, and using techniques such as leverage or momentum to assist in rolling over the step.

5. Are there any real-world applications of minimum force?

Yes, minimum force is a key concept in engineering and mechanics, and is often used in designing structures and machines to be more efficient and require less force to operate. It is also important in sports and physical activities, where minimizing force can help improve performance and prevent injuries.

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