How Does a Scale Determine the Mass of a Student on a Beam?

[brentwoodbc]

A student stands on a uniform 25 kg beam.
The scale on the right reads 350 N. What is the mass of the student?

Answer is 58Kg.

I don't understand what is the deal with the scale? I think I figured this out but I'm not sure.
The force of the scale is opposite the force of the beam, girl right? If so why?
Isn't the force on the centre of rotation equal to the force on the scale?

 

[Redbelly98]

A student stands on a uniform 25 kg beam.
The scale on the right reads 350 N. What is the mass of the student?

Answer is 58Kg.

I don't understand what is the deal with the scale? I think I figured this out but I'm not sure.
The force of the scale is opposite the force of the beam, girl right? If so why?

Well, the force of the beam on the scale is opposite the force of the scale on the beam (Newton's 3rd Law), if that's what you are asking about.

Isn't the force on the centre of rotation equal to the force on the scale?

Not necessarily. That would be true only if the weight were distributed evenly between the centre of rotation and the scale.

A good approach here would be to identify all forces acting on the beam. Then:

• Balance all the forces
• Balance all the torques

The force due to the balance is simply the 350 N reading.

 

[nlightner]

The scale is used to measure the force acting on it, which in this case is the weight of the student. The scale is placed on the right side of the beam because it is acting as a pivot point or fulcrum for the beam. According to the principle of equilibrium, the sum of all forces acting on an object must equal zero for it to be in a state of equilibrium. In this scenario, the force of the student's weight (350 N) is balanced by the opposite force of the scale (350 N). This means that the net force acting on the beam is zero, allowing the beam to remain in a state of equilibrium.

To calculate the mass of the student, we can use the equation F = ma, where F is the force (350 N), m is the mass of the student, and a is the acceleration due to gravity (9.8 m/s^2). Rearranging the equation, we get m = F/a. Plugging in the values, we get m = 350 N / 9.8 m/s^2 = 35.71 kg. However, this is not the mass of the student, as the beam itself has a mass of 25 kg. So, the mass of the student can be calculated by subtracting the mass of the beam from the total mass, which is 35.71 kg - 25 kg = 10.71 kg. Therefore, the mass of the student is approximately 10.71 kg or 58 kg.