EFFECTS OF FORCES

Force changes motion

Hooke’s law Hooke’s Law = law of elasticity by Robert Hooke Hooke’s law states that the extension produced in the spring is proportional to the force exerted. In symbol: F = k x d F = Force (Newtons) k = constant spring d = elongation (meter) or extension The force exerted by the spring is always in the direction to its displacement (elongation) from the equilibrium position. A spring always wants to return to its original position. The spring force is commonly called as restoring force.

Hooke’s law applies to the idealized case of a spring Hooke’s law applies to the idealized case of a spring. The further you stretch the spring, the greater the force opposing the stretching. It assumes that the force increases linearly with distance.

In the figure below, the first spring is still unstretched In the figure below, the first spring is still unstretched. When a force is applied, this results to an elongation x. As the force is doubled, the elongation x is also doubled.

In the y-axis, the force in N is indicated In the y-axis, the force in N is indicated. The force measures from 1 N to 4 N. In the x-axis, the extension or elongation in m is indicated. It shows that the elongation measures 0.1 to 0.4. At 1N of force, the extension is 0.1 m. At 2N force, extension is 0.2m; 3N is 0.3m at 4N force, the extension is 0.4m

Sample Problems If a force of 53 N stretches a spring 8 cm with the force, what is the constant of elasticity or k? How far will the spring stretch when a force of 133 N is applied? Force = constant x elongation F = k x d Solution: Given: Force = 53 N elongation = 8 cm or 8 cm --- change to meter 8 / 100 = .08 m (1 m=100 cm) k = Force / elongation k = 53N / .08 m = 662.5

k = 662.5 F = 133N elongation = ? elongation = F / k elongation = 133 / 662.5 elongation (d) = 0.20 m

Elastic Body and plastic body Elastic body – substances which regains or change back to its original shape and size after moving the force applied to it. Plastic body – substances or objects which completely looses its original shape and size after removing the force applied to it.

Examples of elastic bodies Steel ball – perfectly elastic – it absorbs energy and gives back the energy when a force is removed from it.

IGCSE Sample Problem 1: Set up the experiment to find the spring constant of a steel spring. The apparatus is shown in Fig. 1.1. The student recorded the un-stretched length lo of the spring. The she added loads W to the spring, recording new length l each time. The readings are shown in the table. The un-stretched length lo = 30 mm.

Sample problems – igcse

Weight or Force (N) Length – l (mm) Elongation (mm) 30 mm e = 30 mm – 30 mm = 0 1 32 mm e = 32 mm – 30 mm = 2 mm 2 33 mm e = 33 mm – 30 mm = 3 mm 3 36 mm e = 36 mm – 30 mm = 6 mm 4 39 mm e = 39 mm – 30 mm = 9 mm 5 40 mm e = 40 mm – 30 mm = 10 mm 6 42 mm e = 42 mm – 30 mm = 12 mm Calculate the extension e of the spring produced by each load, using the equation e = (l – lo) or elongation = new length – un-stretched length At F = 0; the elongation e = 30 mm – 30 mm = 0 At F = 1N; e = 32 mm – 30 mm = 2 mm;

Let us use the data above to construct the graph Let us use the data above to construct the graph. The y-axis denotes the elongation in mm. The x-axis represents the weight or load in N. elongation (mm) 12 10 8 6 4 2 0 1 2 3 4 5 6 Load W in Newtons

Draw a straight line of the points you plotted Draw a straight line of the points you plotted. Calculate the gradient of the line. Gradient of the elongation – load graph: = spring constant elongation Gradient = --------------- = spring constant k load 2 Gradient = ------ = 2 1 gradient = 3-2 / 2-1 = 1/1 = 1 gradient = 6-3 / 3-2 = 3/1 = 3 gradient = 9 – 6 / 4-3 = 3/1 = 3 gradient = 10-9 / 5-4 = 1/1 = 1 gradient = 12 – 10 / 6-5 = 2/1 = 2

An IGCSE student is investigating the relationship between the extension of a spring of un-stretched length lo and the load hung on the spring.

a) Consider the readings that the student should take and write appropriate column headings with units in the table below.

b) The student decides to repeat the experiment using a spring made of a different metal in order to study how the extension may be affected by the metal from which the spring is made. To make a fair comparison, other variables must be kept constant. What are some of the variables that the student may be made constant? Length of spring Diameter or thickness of spring Range of loads Length of wire Thickness of wire Number of coils Spacing of coil

Additional Problems 1.

2.

3.

4.

5.