Equivalent forces derivation problem.
EXAMPLE:
Derive the formula for F3 in terms of the experimentally measured quantities m1, m2, 1, and 2.
[Answer: F3=m1gcos1+m2gcos2.]
Make sure you understand how this formula was derived.
QUESTION:
If the mass of both weights is 150 gm, the first mass is located 20 degrees north of east, the second mass is located 20 degrees south of east, and the transducer sensitivity is 0.5 volts/Newton, how large a voltage do you expect to measure? Assume the transducer has been properly zeroed so that V = 0 when F3=0.
The answer should be in volts.
Thank you!
Correction: it should be F3=m1gcos(theta1)+m2gcos(theta2)
what kind of answer is that
Judy posted the question. Judy made a mistake so she commented with corrections. It's not an answer idiot.
To calculate the voltage expected to be measured, we need to first determine the value of F3 using the given information, and then convert it into voltage using the transducer sensitivity.
From the given information, we know:
- The mass of both weights is 150 gm (grams).
- The first mass is located 20 degrees north of east.
- The second mass is located 20 degrees south of east.
To calculate the force F3, we can use the formula F3 = m1gcos1 + m2gcos2, as mentioned in the previous example.
Let's break down the derivation of the formula:
1. Consider a coordinate system in which east is positive x-direction, and north is positive y-direction.
2. The first mass (m1) is located 20 degrees north of east. This means its angle with the positive x-axis is 70 degrees (90 degrees - 20 degrees).
3. The second mass (m2) is located 20 degrees south of east. This means its angle with the positive x-axis is -20 degrees.
4. Now, using the formula F3 = m1gcos1 + m2gcos2, we can substitute the given angles and masses into the formula:
F3 = m1gcos(70 degrees) + m2gcos(-20 degrees)
5. Since cos(-20 degrees) is equal to cos(20 degrees), we can simplify the equation further:
F3 = m1gcos(70 degrees) + m2gcos(20 degrees)
Now, let's calculate the value of F3 using the given information.
Given:
m1 = 150 gm
m2 = 150 gm
transducer sensitivity = 0.5 volts/Newton
Assuming the acceleration due to gravity (g) is approximately 9.81 m/s^2, we can calculate F3 as follows:
F3 = (m1 * g * cos(70 degrees)) + (m2 * g * cos(20 degrees))
= (150 gm * 9.81 m/s^2 * cos(70 degrees)) + (150 gm * 9.81 m/s^2 * cos(20 degrees))
Note: We need to convert the mass from grams to kilograms, so 150 gm is equal to 0.15 kg.
F3 = (0.15 kg * 9.81 m/s^2 * cos(70 degrees)) + (0.15 kg * 9.81 m/s^2 * cos(20 degrees))
Now, let's calculate the values of cos(70 degrees) and cos(20 degrees) using a calculator:
cos(70 degrees) ≈ 0.3420
cos(20 degrees) ≈ 0.9397
Substituting the values into the equation:
F3 = (0.15 kg * 9.81 m/s^2 * 0.3420) + (0.15 kg * 9.81 m/s^2 * 0.9397)
F3 ≈ 1.622 N
Now that we have calculated the force F3 in Newtons, we can convert it into voltage using the transducer sensitivity of 0.5 volts/Newton.
Voltage = F3 * transducer sensitivity
= 1.622 N * 0.5 volts/Newton
Voltage ≈ 0.811 volts
Therefore, the expected voltage measurement is approximately 0.811 volts.