Dabour Hub EGEgyptian Curriculum 2026/2027
2-2 (c) Adding, removing and cutting

2-2 (c) Adding, removing and cutting

Point 3 of 7 — Connected Bodies: Pulleys, Tables, Inclined Planes and Pulley ReactionQuestion bank: 0 questions (0 with pictures)

03 2-2 (c) Adding, removing and cutting

Extra mass on one side

  • If a mass m3 rests on m1 and m1+m3>m2: (m1+m3)a=(m1+m3)g−T and m2a=T−m2g.
  • The tension in a string joining m3 to m1 (if tied rather than resting) is found from the equation of m3 alone: m3a=m3g−T′.
  • When equal masses m hang on both sides and a small mass m′ is added to one, a=m′g2m+m′.

When the extra mass is removed

  • After removal the velocity is the velocity at that moment; the acceleration changes to the new value and may be negative (a deceleration).
  • The system stops instantaneously if the new acceleration is a deceleration, then reverses.
  • If the remaining masses are equal, the system continues at a constant velocity.

When the string is cut

  • Each body then moves under gravity only: a=g downward, whatever its direction of motion.
✍️ Worked examples

Example 5:

  • A 30 g mass hangs on one side of a smooth pulley; two 20 g masses hang tied together on the other side.
  • After 2 s one of the 20 g masses is removed.
  • Find the total distance travelled by the 30 g mass until it first comes to rest.

Solution:

  • Stage 1: a=40−3070×980=140 cm/s2 (the 40 g side goes down).
  • After 2 s: v=280 cm/s and s1=12(140)(4)=280 cm.
  • Stage 2: masses 30 g and 20 g with 30 g now heavier: a′=20−3050×980=−196 cm/s2.
  • It comes to rest after s2=28022×196=78 400392=200 cm.
  • The 30 g mass rises s1+s2=480 cm before coming to rest, then reverses.

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