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We assume a pseudo force on the body being studied in the accelerated frame. The magnitude of pseudo force is equal to the product of mass and acceleration of the frame of reference. It acts in the direction opposite to the acceleration of the frame of reference. While writing equation of motion, we also incorporate this force. But, we use acceleration of the body with respect to accelerated frame of reference - not with respect to inertial frame. This scheme is easily understood with an example. Considering the case as above, let us analyze the motion of block "1". Let us assume that moving pulley is accelerating upwards.

Here, pseudo force is :

Pseudo force

Force analysis in accelerated frame of reference

F s = m 1 a B

The pseudo force is acting in downward direction as the moving pulley "B" is accelerating upward. Now, applying Newton's second law of motion , we have :

T m 1 g m 1 a B = a 1 B

T m 1 g = m 1 ( a 1 B + a B ) = m 1 a 1

Thus, we see that analyzing motion in accelerated frame with pseudo force is equivalent to analyzing motion in inertial frame.

Advantages of analysis in moving frame of reference

The consideration of relative acceleration as against absolute acceleration for analysis using constraint relation (see Pulleys ) has many advantages. We enumerate these advantages here as :

1 : The relative accelerations of blocks with respect to moving pulley are equal in magnitude, but opposite in direction. This is based on the fact that blocks are attached with a single string that passes over moving pulley. This simplifies analysis a great deal.

On the other hand, if we refer accelerations to the ground, then we can not be sure of the directions of accelerations of the blocks as they depend on the acceleration of the pulley itself. It is for this reason that we generally assume same direction of absolute accelerations of the blocks. If the assumption is wrong, then we get negative value of acceleration after analysis, showing that our initial assumption about the direction was wrong and that the acceleration is actually opposite to that assumed. This technique was illustrated in the module on Pulleys .

2 : Sometimes observed values are given in terms of relative reference in the first place. In this situation, we have the easy option to carry out analysis in the accelerated reference itself. Otherwise, we would be required to convert given values to the ground reference, using concept of relative acceleration and carry out the analysis in the ground reference.

Transition between absolute and moving reference

We enumerated advantages of relative acceleration technique. It does not, however, mean that analysis of motion in ground reference has no virtue. As a matter of fact, we are interested in the values, which are referred to ground reference – measurement of accelerations as seen in the ground reference. Even though, relative acceleration technique allows us to simplify solution; the analysis in accelerated frame essentially yields values, which are referred to the accelerated frame of pulley. Ultimately, we are required to convert the solution or values of acceleration in the ground reference.

On the other hand, we have seen in earlier module (see Pulleys ) that the technique of constraint relation is extremely effective. It relates velocities and accelerations of the elements of the system in the ground reference very elegantly – notwithstanding the complexity of the system.

It emerges from above discussion that two frameworks of analysis have their relative strengths and weaknesses. It is, therefore, pragmatic to combine the strengths of two techniques in our analysis. We may transition between two analysis frameworks, using the concept of relative acceleration in one dimension.

a 12 = a 1 a 2

The emphasis on the sequence of subscript almost makes the conversion mechanical. It is always helpful to read the relation : “the relative acceleration of “1” with respect to “2” is equal to the absolute acceleration of “1”, subtracted by the absolute acceleration of “2”.

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
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John Reply
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Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
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David Reply
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David
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emma Reply
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Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
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Adjanou
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Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
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Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
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Mohammed
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Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
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Source:  OpenStax, Physics for k-12. OpenStax CNX. Sep 07, 2009 Download for free at http://cnx.org/content/col10322/1.175
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