To solve the problem of finding the moment caused by the 100-pound (100#) weight about the center of the wheel and to determine the required force $P$ to resist this moment, we need to perform the following steps:

1. Determine the Moment about the Wheel's Center:

The moment of a force about a point is given by:

$\text{Moment} = \text{Force} \times \text{Perpendicular distance to the point}$

• The weight $W = 100 \text{ lb}$ acts vertically downward.
• The perpendicular distance from the center of the wheel to the line of action of the weight is given as $20 \text{ in}$. This is the horizontal distance from the wheel to where the weight acts.

So, the moment $M$ about the center of the wheel due to the weight is:

$M = W \times \text{Perpendicular distance} = 100 \text{ lb} \times 20 \text{ in}$

Now, let's calculate this moment.

2. Determine the Force $P$ to Resist the Moment:

To resist the moment, the force $P$ should create an equal and opposite moment about the wheel's center.

• The force $P$ acts vertically upward, and the distance from the center of the wheel to where $P$ acts is given as $40 \text{ in}$.
• To balance the moment, the moment created by $P$ should equal the moment created by the weight $W$:

$P \times 40 \text{ in} = 100 \text{ lb} \times 20 \text{ in}$

We can solve for $P$.

Let's calculate both the moment and the required force $P$.### Results:

1. Moment of the 100 lb weight about the center of the wheel: $\text{Moment} = 2000 \text{ lb-in}$

2. Force $P$ required to resist this moment: $P = 50 \text{ lb}$

This means a 50 lb upward force at a distance of 40 inches from the wheel will balance the moment caused by the 100 lb weight.

Would you like more details on this calculation or have any additional questions?

5 Related Questions:

1. What would happen to the required force $P$ if the distance to its application point increased?
2. How does the direction of the applied force $P$ affect the moment balance?
3. What other factors, such as friction, could influence the real-world force required?
4. How would the calculation change if the angle of the handles were different?
5. What if the weight $W$ was distributed unevenly?

Tip:

Always consider the direction of forces and distances carefully when calculating moments—moments can be either clockwise or counterclockwise.