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sammy gerbil
sammy gerbil
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Although Block B rests on Block A, the motion of Block B does not affect the motion of Block A, since there is no friction between them. The only forces on Block A are two tension forces in the string.

So you can imagine that Block B rests on the smooth table, instead of on Block A. Both Blocks A and B then slide on the smooth table. Block A is attached to the 2 small pulleys, and can be lumped with them into a single pulley which slides to the right, as in Farcher's diagram.

A word of caution : unlike the pulleys Block A does not rotate, so the "giant pulley" idea could not be used if the rotational KE of the pulleys had to be taken into account.

If you don't like the giant pulley idea (I don't), draw separate free-body diagrams for each of Blocks A, B, C. The equations of motion are :
$m_A a_A = 2T$
$m_B a_B = -T$
$m_C a_C = m_C g - T$.
As lucas shows, the accelerations are related by the fixed length of the string.

Although Block B rests on Block A, the motion of Block B does not affect the motion of Block A, since there is no friction between them. The only forces on Block A are two tension forces in the string.

So you can imagine that Block B rests on the smooth table, instead of on Block A. Both Blocks A and B then slide on the smooth table. Block A is attached to the 2 small pulleys, and can be lumped with them into a single pulley which slides to the right, as in Farcher's diagram.

A word of caution : unlike the pulleys Block A does not rotate, so the "giant pulley" idea could not be used if the rotational KE of the pulleys had to be taken into account.

If you don't like the giant pulley idea (I don't), draw separate free-body diagrams for each of Blocks A, B, C.

Although Block B rests on Block A, the motion of Block B does not affect the motion of Block A, since there is no friction between them. The only forces on Block A are two tension forces in the string.

So you can imagine that Block B rests on the smooth table, instead of on Block A. Both Blocks A and B then slide on the smooth table. Block A is attached to the 2 small pulleys, and can be lumped with them into a single pulley which slides to the right, as in Farcher's diagram.

A word of caution : unlike the pulleys Block A does not rotate, so the "giant pulley" idea could not be used if the rotational KE of the pulleys had to be taken into account.

If you don't like the giant pulley idea (I don't), draw separate free-body diagrams for each of Blocks A, B, C. The equations of motion are :
$m_A a_A = 2T$
$m_B a_B = -T$
$m_C a_C = m_C g - T$.
As lucas shows, the accelerations are related by the fixed length of the string.

added 73 characters in body
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sammy gerbil
sammy gerbil
  • 27.5k
  • 6
  • 35
  • 72

You can treat Block A as a giant pulley because, althoughAlthough Block B rests on itBlock A, the motion of Block B does not affect the motion of Block A, since there is no friction between them. The only forces on Block A are two tension forces in the string.

So you can imagine that Block B rests on the smooth table, instead of on Block A. Both Blocks A and B then slide on the smooth table. Block A is attached to the 2 small pulleys, and can be lumped with them into a single pulley which slides to the right, as in Farcher's diagram.

A word of caution : unlike the pulleys Block A does not rotate, so the "giant pulley" idea could not be used if the rotational KE of the pulleys had to be taken into account.

If you don't like the giant pulley idea (I don't), draw separate free-body diagrams for each of Blocks A, B, C.

You can treat Block A as a giant pulley because, although Block B rests on it, the motion of Block B does not affect the motion of Block A, since there is no friction between them. The only forces on Block A are two tension forces in the string.

So you can imagine that Block B rests on the smooth table, instead of on Block A. Both Blocks A and B then slide on the smooth table. Block A is attached to the 2 small pulleys, and can be lumped with them into a single pulley which slides to the right, as in Farcher's diagram.

A word of caution : unlike the pulleys Block A does not rotate, so the "giant pulley" idea could not be used if the rotational KE of the pulleys had to be taken into account.

Although Block B rests on Block A, the motion of Block B does not affect the motion of Block A, since there is no friction between them. The only forces on Block A are two tension forces in the string.

So you can imagine that Block B rests on the smooth table, instead of on Block A. Both Blocks A and B then slide on the smooth table. Block A is attached to the 2 small pulleys, and can be lumped with them into a single pulley which slides to the right, as in Farcher's diagram.

A word of caution : unlike the pulleys Block A does not rotate, so the "giant pulley" idea could not be used if the rotational KE of the pulleys had to be taken into account.

If you don't like the giant pulley idea (I don't), draw separate free-body diagrams for each of Blocks A, B, C.

Source Link
sammy gerbil
sammy gerbil
  • 27.5k
  • 6
  • 35
  • 72

You can treat Block A as a giant pulley because, although Block B rests on it, the motion of Block B does not affect the motion of Block A, since there is no friction between them. The only forces on Block A are two tension forces in the string.

So you can imagine that Block B rests on the smooth table, instead of on Block A. Both Blocks A and B then slide on the smooth table. Block A is attached to the 2 small pulleys, and can be lumped with them into a single pulley which slides to the right, as in Farcher's diagram.

A word of caution : unlike the pulleys Block A does not rotate, so the "giant pulley" idea could not be used if the rotational KE of the pulleys had to be taken into account.