A former student of ENG8101 wishes to weigh him/herself but only has access to a scale
A with capacity limited to 400 N and a small 80-N spring dynamometer B. With the rig
shown, he/she discovers that when he/she exerts a pull on the rope so that B registers 76
N, the scale A reads 268 N. What are his/her correct weight and mass m.
To find the correct weight and mass, we need to use the information given about the scale A and dynamometer B.
First, let's analyze the forces acting on the system:
1. Weight of the person (m * g): This is the force with which the Earth pulls on the person and is equal to the person's weight. Let's denote this force as Fw.
2. Force measured by scale A: When the person exerted a pull on the rope, scale A registered a force of 268 N. Let's denote this reading as FA.
3. Force measured by dynamometer B: When the person exerted a pull on the rope, dynamometer B registered a force of 76 N. Let's denote this reading as FB.
Based on the information given, we can set up the following equations:
FA = Fw - FB ...(Equation 1)
From the information given, we know that FA = 268 N and FB = 76 N. Let's substitute these values into Equation 1:
268 N = Fw - 76 N
Now, we can solve for Fw, which represents the person's weight:
Fw = 268 N + 76 N
Fw = 344 N
The weight of the person is 344 N.
To find the mass of the person, we can use the equation:
Fw = m * g ...(Equation 2)
We know that Fw = 344 N, and the acceleration due to gravity g is approximately 9.8 m/s². Let's substitute these values into Equation 2:
344 N = m * 9.8 m/s²
Now, we can solve for m, which represents the person's mass:
m = 344 N / 9.8 m/s²
m ≈ 35.1 kg
Therefore, the correct weight of the person is 344 N, and the mass is approximately 35.1 kg.