Lesson Worksheet: Hooke’s Law Mathematics

A uniform rod of mass 3.5 kg and length 4 m is fixed at , while its other end is connected by an elastic string, with a modulus of elasticity 11.1 N, to a point , which lies at the same height as , and 5.8 m from it. The system is in equilibrium when . Taking , 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 particle of mass 1 kg is attached to point 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 and released from rest. Find the initial acceleration of the particle. Consider the acceleration due to gravity to be 9.8 m/s².

A bead of mass 742 g hangs from a ceiling by a light elastic string 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 and that the bead is moving in a horizontal circle such that the string is inclined at to the vertical, find the angular speed of the bead in radians per second correct to one decimal place. Take .

is a fixed point on a rough plane, inclined at angle to the horizontal, where . An elastic string of natural length 2.8 m and modulus of elasticity 37.6 N is attached to at one end and a ball of mass 2.5 kg at the other end. Given that the ball was held at 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 .

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

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.

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