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Lesson: Equilibrium of Forces and Hooke's Law

Worksheet • 6 Questions

Q1:

A ball of mass 0.5 kg hangs in equilibrium from the ceiling by a light elastic spring of natural length 1.2 m and a modulus of elasticity 9.8 N. How much energy is stored in the spring? Take 𝑔 = 9 . 8 / m s 2 .

Q2:

An elastic string of natural length 4 m and modulus of elasticity 8 N is stretched to a length of 4.5 m. How much energy is stored in the stretched string?

Q3:

A ball of mass 1.8 kg is attached to one end of a light elastic string of natural length 2.4 m and modulus of elasticity 17.1 N. The other end of the string is fixed at a point 𝑂 . The ball is released from rest at 𝑂 . Taking 𝑔 = 9 . 8 / m s 2 , find how far below 𝑂 the ball reaches before coming instantaneously to rest.

Q4:

A particle of mass 4 π‘š hangs in equilibrium at the end of an elastic string of natural length 6 π‘Ž connected to a ceiling. The length of the string is then 8 π‘Ž . Find the elastic potential energy stored in the string. Consider the acceleration due to gravity to be 𝑔 .

  • A 4 π‘š 𝑔 π‘Ž
  • B 1 2 π‘š 𝑔 π‘Ž
  • C 8 π‘š 𝑔 π‘Ž
  • D 1 6 π‘š 𝑔 π‘Ž
  • E 2 π‘š 𝑔 π‘Ž

Q5:

A uniform rod 𝐴 𝐡 of mass 3.5 kg and length 4 m is fixed at 𝐴 , while its other end 𝐡 is connected by an elastic string, with a modulus of elasticity 11.1 N, to a point 𝐢 , which lies at the same height as 𝐴 , and 5.8 m from it. The system is in equilibrium when ∠ 𝐴 𝐡 𝐢 = 9 0 ∘ . Taking 𝑔 = 9 . 8 / m s 2 , find the tension in the elastic string when the system is in equilibrium, and hence find its natural length. Give your answers correct to two decimal places.

  • A 𝑇 = 1 1 . 8 3 N, 𝑙 = 2 . 0 3 m
  • B 𝑇 = 2 . 4 1 N, 𝑙 = 3 . 4 5 m
  • C 𝑇 = 1 1 . 8 3 N, 𝑙 = 1 . 3 4 m
  • D 𝑇 = 2 3 . 6 6 N, 𝑙 = 2 . 0 3 m
  • E 𝑇 = 2 3 . 6 6 N, 𝑙 = 1 . 3 4 m

Q6:

One end of a light elastic string is attached to a fixed point. A force of 3.8 N is applied to the other end of the string to stretch it. The natural length of the string is 2.8 m, and its modulus of elasticity is 26.6 N. Find the total length of the stretched string.

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