Wednesday, 5 March 2014

(O Level Phy) Trolley pulled by a weight over a pulley

Example: An 8 kg trolley is pulled along a horizontal bench surface by a string that is connected to a 2 kg weight over a frictionless pulley. The friction between the trolley and the bench surface is 16 N. Calculate the (a) acceleration of the system (b) the tension T in the string.

Cambridge O Level Physics examinations rarely test such questions which look more like A Level questions than O Level questions. Secondary schools, especially the so called “good schools”, however, like to challenge and stretch students. In solving such a question, you need to decide whether to consider the system as a whole or just the trolley or the weight. When I say the system as a whole, I am really referring to the entire system which includes both the trolley and the weight. Next, identify the forces acting on the system or object you've isolated and then apply ∑F = ma (from Newton's Second Law).

Decide whether to look at the entire system as a whole OR isolate either the trolley or the weight
Identify the forces acting on the system or object… 
Apply ∑F = ma...



Try these questions before you check with the answers below.

  1. A box of trolley m1 is pulled by a string that is connected to a mass m2 over a frictionless pulley. The friction between m1 and the table surface is equal to µ x weight of m1 where µ is a constant. Find an expression for the acceleration a of the system.
  2. A 5.00 kg trolley placed on a frictionless horizontal bench surface is connected to a string that passes over a frictionless pulley. The string is hung with a 9.00 kg mass. Find the (a) acceleration of the trolley (b) tension in the string.

Answers: 1. The friction between m1 and table surface = µm1g. Weight of m2 = m2g. Consider the whole system. ∑F = (m1 + m2)a ==> m2g – µm1g = (m1 + m2)a ==> a = (m2g – µm1g)/(m1 + m2) 2. Consider the whole system. ∑F = W – f = total mass x acceleration ==> 9 kg x 10 N/kg – 0 = (5 kg + 9 kg) x a ==> a = 6.43 m/s2 (b) Consider only the trolley. T – f = T – 0 = 5 kg x 6.43 m/s2 ==> T = 32.2 N. Or we consider only the weight. W – T = 9 kg x 10 N/kg – T = 9 kg x 6.43 m/s2 ==> T = -32.2 N 

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