Starting with "m1g - T1 = m1a ", "T2 - m2g = m2a" and "(T1 -...

Starting with

"m1g - T1 = m1a ", "T2 - m2g = m2a" and "(T1 - T2) R = I ?"

show the derivation steps of

"(m1 - m2)g = (m1 + m2 + I/R^2) a

Expert Solution

Consider the Atwood machine shown at the right. It is an example of pure rotational motion; that is, the center of gravity of the pulley does not translate up/down or to the left/right.

The equations of motion for an Atwood machine that has a pulley with rotational inertia are:

For the smaller mass:

net F = ma
T₁ - mg = ma

For the larger mass:

net F = ma
Mg - T₂ = Ma

For the pulley:

net ? = I_CM?
(T₂ - T₁)r = I?

In this case net torque is calculated by finding the product of (T₂ - T₁)r where T₂ is the tension in the direction of the pulley's rotation (towards the larger mass) and T₁ is the tension in the cord on the other side of the pulley. The radius of the pulley is r. Once again, remember that T₁ and T₂ can only be equal if the pulley is "massless and frictionless."

The equation a = r? will allow you to relate the linear acceleration of the hanging masses with the angular acceleration of the pulley.

genius_generous answered 2 years ago

Two solid bodies at initial temperatures T1 and T2, with T1 > T2, are placed in...

Two solid bodies at initial temperatures T1 and T2, with T1 > T2, are placed in thermal contact with each other. The bodies exchange heat only with eachother but not with the environment. The heat capacities C ≡ Q/∆T of each body are denoted C1 and C2, and are assumed to be positive. (a) Is there any work done on the system? What is the total heat absorbed by the system? Does the internal energy of each subsystem U1 and...

If T1 , T2 : Rn → Rm are linear maps with range(T1) = range(T2), show...

If T1 , T2 : Rn → Rm are linear maps with range(T1) = range(T2), show that there exists an invertible linear map U:Rn →Rn so that T1=U◦T2

ON PYTHON: a) Write a function named concatTuples(t1, t2) that concatenates two tuples t1 and t2...

ON PYTHON: a) Write a function named concatTuples(t1, t2) that concatenates two tuples t1 and t2 and returns the concatenated tuple. Test your function with t1 = (4, 5, 6) and t2 = (7,) What happens if t2 = 7? Note the name of the error. b) Write try-except-else-finally to handle the above tuple concatenation problem as follows: If the user inputs an integer instead of a tuple the result of the concatenation would be an empty tuple. Include an...

On Python: a) Write a function named concatTuples(t1, t2) that concatenates two tuples t1 and t2...

On Python: a) Write a function named concatTuples(t1, t2) that concatenates two tuples t1 and t2 and returns the concatenated tuple. Test your function with t1 = (4, 5, 6) and t2 = (7,) What happens if t2 = 7? Note the name of the error. b) Write try-except-else-finally to handle the above tuple concatenation problem as follows: If the user inputs an integer instead of a tuple the result of the concatenation would be an empty tuple. Include an...

Suppose T1 and T2 are iid Exp(1). What is the probability density function of T1+T2? What...

Suppose T1 and T2 are iid Exp(1). What is the probability density function of T1+T2? What is the probability that T1+T2 ≥ 3?

Show that, for a Carnot engine operating between reservoirs at temperatures T1 and T2 (T1 >...

Show that, for a Carnot engine operating between reservoirs at temperatures T1 and T2 (T1 > T2), the thermal efficiency is given by Eta sub R = T1-T2/T1

Consider the following history H: T2:R(Y), T1:R(X), T3:R(Y), T2:R(X), T2:W(Y), T2:Commit, T1:W(X), T1:Commit, T3:R(X), T3:Commit Assume...

Consider the following history H: T2:R(Y), T1:R(X), T3:R(Y), T2:R(X), T2:W(Y), T2:Commit, T1:W(X), T1:Commit, T3:R(X), T3:Commit Assume that each transaction is consistent. Does the final database state satisfy all integrity constraints? Explain.

The following is the original code, (add, t1, 3, 5) (assign, a, t1) (add, t2, 3,...

The following is the original code, (add, t1, 3, 5) (assign, a, t1) (add, t2, 3, 5) (sub, t3, t2, z) (assign, b, t3) Constant folding is applied to give the following, (assign, t1, 8) (assign, a, t1) (assign, t2, 8) (sub, t3, t2, z) (assign, b, t3) After the constant folding is applied, the (assign, t2, 8) becomes redundant. What optimizations should take place in order to remove this redundancy in the constant folded code? Also show the optimized...

Find the data hazards in the following code segment lw $t1,0($t1) addi $t1,$t1,100 or $t2,$t3,$t1 add...

Find the data hazards in the following code segment lw $t1,0($t1) addi $t1,$t1,100 or $t2,$t3,$t1 add $a0,$a1,$t2 ori $a0,$a0,42 add $t5,$a0,$t2 Reorder the following code segment to remove the data hazards. Assume that data forwarding takes place: lw $t0,24($a0) sub $t4,$t4,$t0 sub $t8,$t8,$t3 add $t6,$t6,$t5 mul $t7,$t7,$t1 What is the CPI for the reordered sequence of instructions in the preceding problem?

Three instructors in a coordinated course, T1, T2, and T3 evaluates axam papers. T1 evaluates 20%...

Three instructors in a coordinated course, T1, T2, and T3 evaluates axam papers. T1 evaluates 20% of the exam papers, T2 pevaluates 30% and T3 evaluates 50%. The three theachers make the following proportions of errors (E) while evaluating the exam papers: 0.008, 0.008, and 0.003 respectively. If a randomly selected exam paper has an error (E), what is the probability it is from instructor T1?

Question