Lesson Worksheet: Applications of Newton’s Second Law: Two Masses Hanging from a Pulley Mathematics

In this worksheet, we will practice solving problems on the motion of a system of two bodies suspended vertically by a string passing over a smooth pulley.

Q1:

Two bodies of masses 12 kg and 18 kg are attached to the ends of a light inextensible string which passes over a smooth pulley. Determine the acceleration of the system. Take 𝑔=9.8/ms.

Q2:

Two masses 𝑚 and 88 g are attached to the ends of a light string passing over a smooth pulley. Determine the value of 𝑚, given that, when the system was released, the other mass descended 11.76 m in 2 seconds. Take the acceleration due to gravity 𝑔=9.8/ms.

Q3:

Two masses of 143 g and 77 g are connected to the ends of a light inextensible string passing over a fixed smooth pulley. Given that the two masses were hanging freely vertically below the pulley and that the system was released from rest, find its velocity 4 seconds later. Take 𝑔=9.8/ms.

Q4:

Two masses of 5𝑚 and 2𝑚 kilograms are connected to each other by a light inextensible string passing over a smooth pulley. Given that the system was released from rest and that the force exerted on the pulley during the motion was 238 N, determine the value of 𝑚. Take 𝑔=9.8/ms.

Q5:

Two bodies of masses 𝑚 g and (𝑚+56) g are connected to each other by a light string which passes over a fixed smooth pulley. The system was released from rest when the two bodies were at the same horizontal level. One second later, the vertical distance between them was 128 cm. Find the magnitude of the force exerted on the pulley while the bodies were in motion. Take the acceleration due to gravity 𝑔=9.8/ms.

Q6:

Two bodies of masses 270 and 𝑚 grams are connected by two ends of a string passing over a smooth pulley. The body of mass 𝑚 was projected downward at 105 cm/s and, 3 seconds later, it returned to its initial position. Find the value of 𝑚 and the tension 𝑇 in the string. Take 𝑔=9.8/ms.

  • A𝑚=234g, 𝑇=2.457N
  • B𝑚=242g, 𝑇=5.103N
  • C𝑚=234g, 𝑇=2.835N
  • D𝑚=270g, 𝑇=2.835N

Q7:

Two bodies, 𝐴 and 𝐵, of equal mass 𝑚 grams were connected to one another by means of a light inextensible string which passed over a smooth pulley. A mass of 44 g was added to body 𝐴 and the system was released from rest. Body 𝐴 hit the ground after moving 64 cm, whereas body 𝐵 continued its motion upward until it momentarily came to rest 80 cm above its starting point. Find the value of 𝑚, given that the acceleration due to gravity 𝑔=9.8/ms.

Q8:

Two bodies of masses 644 g and 156 g were connected to the ends of a light inextensible string passing over a smooth pulley. The system was released from rest and, 2 seconds later, the larger mass hit the ground. Find the maximum height the smaller mass reached above its initial position. Take the acceleration due to gravity 𝑔=9.8/ms.

Q9:

Two bodies of masses 8.7 and 11.6 grams hung vertically from the ends of a light inextensible string passing over a smooth pulley. When the bodies were released from rest, they were on the same horizontal level. Determine the vertical distance between them one second after they started moving. Take the acceleration due to gravity 𝑔 to be 9.8 m/s2.

Q10:

Two bodies of masses 374 g and 102 g were connected to each other by a light inextensible string passing over a smooth pulley. The two bodies started at rest on the same horizontal level. Then one second after the system was released, the string broke. Determine the vertical distance between the two bodies one second after the string broke. Take the acceleration due to gravity 𝑔=9.8/ms.

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