Lesson Worksheet: Hooke’s Law Mathematics

In this worksheet, we will practice finding the force of stretching or compressing an elastic string or elastic spring using Hooke’s law.

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/ms.

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/ms, find how far below 𝑂 the ball reaches before coming instantaneously to rest.

Q4:

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

  • A12𝑚𝑔𝑎
  • B2𝑚𝑔𝑎
  • C16𝑚𝑔𝑎
  • D8𝑚𝑔𝑎
  • E4𝑚𝑔𝑎

Q5:

A uniform rod 𝐴𝐵 of mass 3.5 kg and length 4 m is fixed at 𝐴, while its other end 𝐵 is connected by an elastic string, with a modulus of elasticity 11.1 N, to a point 𝐶, which lies at the same height as 𝐴, and 5.8 m from it. The system is in equilibrium when 𝑚𝐴𝐵𝐶=90. Taking 𝑔=9.8/ms, 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.

  • A𝑇=11.83 N, 𝑙=1.34 m
  • B𝑇=2.41 N, 𝑙=3.45 m
  • C𝑇=23.66 N, 𝑙=1.34 m
  • D𝑇=23.66 N, 𝑙=2.03 m
  • E𝑇=11.83 N, 𝑙=2.03 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.

Q7:

A particle of mass 1 kg is attached to point 𝑂 on horizontal ceiling by a light elastic string of natural length 0.6 m and modulus of elasticity 18 N. The particle is held at a distance of 1.3 m directly below point 𝑂 and released from rest. Find the initial acceleration of the particle. Consider the acceleration due to gravity to be 9.8 m/s2.

Q8:

A bead of mass 742 g hangs from a ceiling by a light elastic string 𝐴𝐵 with a natural length of 2 m and a modulus of elasticity of 20 N. Given that the string is fixed to the ceiling at point 𝐴 and that the bead is moving in a horizontal circle such that the string is inclined at 14 to the vertical, find the angular speed of the bead in radians per second correct to one decimal place. Take 𝑔=9.8/ms.

Q9:

𝑂 is a fixed point on a rough plane, inclined at angle 𝛼 to the horizontal, where tan𝛼=0.65. An elastic string of natural length 2.8 m and modulus of elasticity 37.6 N is attached to 𝑂 at one end and a ball of mass 2.5 kg at the other end. Given that the ball was held at 𝑂 and then released from rest, coming to a stop again after moving 5.6 m down the plane, find the coefficient of friction between the ball and the plane to two decimal places. Take 𝑔=9.8/ms.

Q10:

A rod 𝐴𝐵 has mass 4𝑚 and length 2𝑎. The rod rests horizontally in equilibrium, and is suspended from a fixed point 𝐶 by two light strings 𝐴𝐶 and 𝐵𝐶. 𝐴𝐶 makes an angle 𝛼 with the rod and is perpendicular to 𝐵𝐶, as shown in the figure. The string 𝐵𝐶 is elastic, with a natural length 𝑎 and a modulus of elasticity 𝑘𝑚𝑔. Assume 𝑘 is a constant and 𝑔 is the acceleration due to gravity. Find the value of 𝑘.

This lesson includes 17 additional questions and 211 additional question variations for subscribers.

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