Question

You are designing a circuit for an experimental setup where you have a force sensor that will experience a load between 8N and 15N. Over this range the force sensor outputs a voltage that is linearly proportional to the applied force and provides an output of 2.2V to 2.9V.

You are collecting the data with an Arduino which has a 10-bit analog-to-digital (A2D) converter that measures voltages between 0V and 5V. You want to measure the applied force with as high a resolution as possible. You can assume that the op-amp power supplies are +15V and -15V.

(a) Calculate the resolution in Newtons (N) if you directly connected the force sensor to the Arduino A2D pin.

Answer 1

The resolution in Newtons (N) when directly connecting the force sensor to the Arduino A2D pin is approximately 0.0008004N.

Step-by-step explanation:

To calculate the resolution in Newtons (N) when directly connecting the force sensor to the Arduino A2D pin, we need to determine the voltage range that corresponds to the force range.

The force sensor provides an output voltage of 2.2V to 2.9V over the force range of 8N to 15N.

We can calculate the voltage resolution by subtracting the minimum voltage from the maximum voltage: 2.9V - 2.2V = 0.7V.

Since the Arduino's analog-to-digital converter (A2D) has a range of 0V to 5V and is 10-bit, the voltage resolution is given by: 0.7V / 2^10 = 0.7V / 1024 = 0.0006836V.

To convert this voltage resolution to the force resolution, we need to determine the proportionality factor between voltage and force.

Since the force sensor outputs a voltage that is linearly proportional to the applied force, we can determine this factor by dividing the force range by the voltage range: (15N - 8N) / (2.9V - 2.2V) = 1.17 N/V.

Finally, we can calculate the force resolution by multiplying the voltage resolution by the proportionality factor: 0.0006836V * 1.17 N/V = 0.0008004N.

Therefore, the resolution in Newtons (N) is approximately 0.0008004N.