Forces in Connected Objects (Systems) Video Lessons

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Problem: Each of the systems shown is initially at rest. Neglecting axle friction and the masses of the pulleys, determine for each system:(a) the acceleration of block A(b) the velocity of block A after it has moved through 10 ft.(c) the time required for block A to reach a velocity of 20 ft/s.

FREE Expert Solution

In this problem, we're going to use Newton's second law of motion, which states:

F=ma, where ΣF is the sum of forces, m is the mass, and a is the acceleration.

We also need to get m in our case. 

m=Wg, where W is weight and g is the acceleration due to gravity.

System 1

(a)

Taking Newton's equation on block A:

Fy=mAaAWA-T=WAgaAT=WA-WAgaA=200-200gaA

T = 200(1 - aA/g) ........................... (1)

Now, consider block B:

Fy=mBaBT-WB=WBgaBT=WB+WBgaB=100+100gaB

T = 100(1 + aB/g) ................. (2)

Let's equate equations (1) and (2) and remember that |aA| = |aB|.

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Problem Details

Each of the systems shown is initially at rest. Neglecting axle friction and the masses of the pulleys, determine for each system:

(a) the acceleration of block A

(b) the velocity of block A after it has moved through 10 ft.

(c) the time required for block A to reach a velocity of 20 ft/s.

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