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 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

Q5:

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.

Q6:

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.

Q7:

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.

Q8:

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.

Q9:

A ball with mass 2.3 kg hangs from the ceiling by a light elastic string with a natural length of 2.4 m and a modulus of elasticity of 29.4 N. Determine the extension of the string, considering the acceleration due to gravity to be 9.8 m/s2.

Q10:

A 4 kg body is hanging in equilibrium and suspended at 𝑃 by two light strings 𝐴𝑃 and 𝐵𝑃. The two strings are attached to two fixed points 𝐴 and 𝐵 on the same horizontal level. 𝐵𝑃 is inextensible, while 𝐴𝑃 is elastic with a natural length of 0.8 m and a modulus of elasticity of 9.8 N. 𝐴𝑃 makes an angle of 30 with 𝐴𝐵, and the two strings make a right angle at 𝑃. Find the length of 𝐵𝑃 and its tension 𝑇. Give both of your answers correct to one decimal place. Take 𝑔=9.8/ms.

  • A𝐵𝑃=0.9m, 𝑇=19.6N
  • B𝐵𝑃=2.8m, 𝑇=33.9N
  • C𝐵𝑃=1.4m, 𝑇=33.9N
  • D𝐵𝑃=1.8m, 𝑇=39.2N
  • E𝐵𝑃=1.4m, 𝑇=19.6N

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