Bending Moment in a Cantilever

A cantilever is a structural element that is supported at one end and protrudes outwards. When a load is applied to the free end of the cantilever, it creates a bending moment along the length of the cantilever. The bending moment is a measure of the internal force that causes the cantilever to bend.

Understanding the Bending Moment

The bending moment at any point along the cantilever is given by the equation:

M = P * l

Where M is the bending moment, P is the load applied at the free end, and l is the span of the cantilever.

In this case, the load is acting at the free end of the cantilever. Therefore, the bending moment at the free end can be determined by substituting the values into the equation:

M = P * l

Since the span of the cantilever is l, the bending moment at the free end is given by:

M = P * l

Simplifying the equation, we find that the bending moment at the free end is equal to the product of the load and the span of the cantilever.

Applying the Load

Now, let's consider the options given:

a) 0
b) P
c) P^2
d) P/2

From the equation for the bending moment, we can see that the correct answer is option a) 0. This means that the bending moment at the free end of the cantilever is zero when the load is applied. This is because the load is acting directly at the free end, causing the cantilever to be in a state of pure bending without any moment at the free end.

Conclusion

In summary, the bending moment at the free end of a cantilever with a load applied at the free end is zero. This is because the load is acting directly at the free end, causing the cantilever to be in a state of pure bending without any moment at the free end.