Theoretical and Actual Acceleration for an Atwood Machine

In summary, the conversation involved discussing the calculation of acceleration and tension using free body diagrams and equations involving mass, gravity, and acceleration. Two trials were conducted, with the first one needing assistance. The formulas used were A=(m2-m1/m1+m2)g for acceleration, Ath=g(m2-m1/m1+m2) for theoretical acceleration, and T=(2m1m2/m1+m2)g for tension. It was clarified that the units should be in kilograms for consistency.
  • #1
Pandaluvv2
3
0

Homework Statement



Include free body diagrams and equations solved independently for acceleration and tension. Note: a and T are to be expressed in terms of m1, m2, and g only.
Trial 1:Mass1= 55g and Mass2= 60g
Trial 2:Mass1= 55g and Mass2= 65g
We are doing 2 trials but i need help with the first one. I'm not sure how to figure out the acceleration and theoretical acceleration, should they be coming out the same?

Homework Equations



A=(m2-m1/m1+m2)g
Ath=g(m2-m1/m1+m2)
T=(2m1m2/m1+m2)g

The Attempt at a Solution



Trial 1: A=((60-55)/(60+55))*9.8 = (5/115)*9.8 = 0.426m/s/s
Ath=9.8*((60-55)/(60+55)) = 9.8*(5/115) = 0.4260m/s/s
T=(2*55*60/55+60)9.8 = (6600/115)*9.8 = 562.43N
 
Last edited:
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  • #2
Hi Pandaluvv2, welcome to Physics Forums.

Is this assignment accompanying a hands-on lab? If so, the "actual acceleration" would be the value you measure during the experiment, which would subsequently be compared to the theoretical value that you calculate.

The formulas that you've arrived at appear to be okay but you need to be careful with the units. Your masses are given in grams but should be converted to kilograms for use in the tension formula. The scaling factors happen to cancel out in the acceleration formula so your result turns out to be correct, but you should be using kilograms there too.
 
  • #3
Okay, that makes sense, I forgot we had found acceleration during class, which would have saved me a bunch of time. The only thing I should change is my mass to kilograms then right? So I can use it for the tension?
 
  • #4
Pandaluvv2 said:
Okay, that makes sense, I forgot we had found acceleration during class, which would have saved me a bunch of time. The only thing I should change is my mass to kilograms then right? So I can use it for the tension?

Yup. Work in kilograms.
 
  • #5
Okay, thank you very much for the help!
 

1. What is an Atwood Machine?

An Atwood Machine is a simple mechanical device consisting of two masses connected by a string or cord that passes over a pulley. It is often used to study the effects of acceleration and tension on objects in motion.

2. What is theoretical acceleration for an Atwood Machine?

The theoretical acceleration for an Atwood Machine is the acceleration that is predicted by theoretical calculations or equations. It is based on the masses of the objects, the force of gravity, and the tension in the string.

3. How is actual acceleration for an Atwood Machine measured?

Actual acceleration for an Atwood Machine is measured by conducting experiments with a physical Atwood Machine and using tools such as a timer and a stopwatch to measure the time it takes for the masses to move a certain distance. The measured acceleration may differ from the theoretical acceleration due to factors such as friction and air resistance.

4. What factors can affect the acceleration of an Atwood Machine?

The acceleration of an Atwood Machine can be affected by several factors, including the masses of the objects, the force of gravity, the tension in the string, and external forces such as friction and air resistance. The length and angle of the string can also impact the acceleration.

5. How is the acceleration of an Atwood Machine used in real-world applications?

The acceleration of an Atwood Machine can be used in real-world applications such as elevators, cranes, and other systems that use pulleys and ropes to lift or move objects. It can also be used in physics experiments to study the principles of motion and forces.

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