A 3m long balance beam is simply supported with an overhang at each end of a=0.5m. A gymnast weighing 50kg is standing a distance c to the right of support A and a distance b to the left of support B. How does the maximum bending moment in the beam depend on the distance c? Express your answer in terms of c assuming units of Nm for the bending moment. Please take the acceleration due to gravity to be 10m/s2.

Mmax=?

500*c-250*c^2

somebody can help?

To determine the maximum bending moment (Mmax) in the beam, we need to consider the weight of the gymnast and the moments generated by that weight on the beam.

First, let's review the concept of a bending moment. In a simply supported beam like this one, the bending moment is the internal moment that develops within the beam due to an external load or force acting on it. The bending moment is expressed in units of Nm (Newton-meter) and is a measure of the amount of bending or deformation occurring in the beam.

In this case, the gymnast's weight generates a force due to gravity. The magnitude of this force is given by:

Force (F) = mass (m) * acceleration due to gravity (g)
F = 50 kg * 10 m/s^2
F = 500 N

Now, let's consider the moments generated by this force at each support point.

At support A:
The weight of the gymnast creates a clockwise moment (M) about support A. The moment generated by the weight acting at a distance of c to the right of A is given by:

M_A = F * c
M_A = 500 N * c

At support B:
The weight of the gymnast creates a counterclockwise moment (M) about support B. The moment generated by the weight acting at a distance of b to the left of B is given by:

M_B = F * b
M_B = 500 N * b

For maximum bending moment, the bending moments at both support A and support B need to be added together. Since they act in opposite directions, their magnitudes should be subtracted:

Mmax = |M_A - M_B|
Mmax = |(500 N * c) - (500 N * b)|
Mmax = |500 N * (c - b)|

Hence, the maximum bending moment (Mmax) in the beam depends on the difference between the distances c and b, multiplied by the weight of the gymnast.

Please note that this answer assumes that the beam is uniform and other external factors, such as dynamic loads or additional forces, are not considered.