I wondered if someone would check my work concerning an Atwood's Machine. (I am led to believe the answers for these two questions should be the same but I'm not coming out that way.)Thank you!
8.) Caluclate the tension in the Atwood's Machine string for the case when m2 is 180 grams and m1 is 220 grams. Assume system is moving freely. The desired tension value is tension in string connected to 220 gram mass.
m1(g) -m2(g) = ma
.220(9.8) -.180(9.8) = .400a
2.156-1.764 = .400a
a=.98m/s^2
T - m1g = ma
T - .220(9.8) = .220(9.8)
T - 2.156 = .2156
T = 2.37
9.) Caluclate the tension in the Atwood's Machine string for the case when m2 is 180 grams and m1 is 220 grams. Assume system is moving freely. The desired tension value is tension in string connected to 180gram mass.
m1(g) -m2(g) = ma
.220(9.8) -.180(9.8) = .400a
2.156-1.764 = .400a
a=.98m/s^2
T - m2g = ma
T - .180(9.8) = .180(9.8)
T - 1.764 = .1764
T = 1.94
To check your work on the Atwood's Machine problem, we need to use the correct equations and calculations.
For question 8:
The equation relating the masses and acceleration in an Atwood's Machine is:
m1(g) - m2(g) = ma
Given:
m1 = 220 grams = 0.22 kg
m2 = 180 grams = 0.18 kg
g = 9.8 m/s^2 (acceleration due to gravity)
Let's calculate the acceleration (a) first:
0.22(9.8) - 0.18(9.8) = 0.4a
2.156 - 1.764 = 0.4a
0.392 = 0.4a
a = 0.392 / 0.4
a = 0.98 m/s^2
Next, calculate the tension (T) in the string connected to the 220 gram mass using the equation:
T - m1g = ma
T - 0.22(9.8) = 0.22(0.98)
T - 2.156 = 0.2156
T = 2.3716 N
So, the tension in the string connected to the 220 gram mass is approximately 2.37 N.
For question 9:
Similarly, let's calculate the acceleration first using the same equation:
0.22(9.8) - 0.18(9.8) = 0.4a
2.156 - 1.764 = 0.4a
0.392 = 0.4a
a = 0.392 / 0.4
a = 0.98 m/s^2
Now, calculate the tension (T) in the string connected to the 180 gram mass using the equation:
T - m2g = ma
T - 0.18(9.8) = 0.18(0.98)
T - 1.764 = 0.1764
T = 1.9404 N
So, the tension in the string connected to the 180 gram mass is approximately 1.94 N.
Therefore, your calculated values for both questions are correct.