1. Hooke\'s Law - experiment report PDF

Preview

Summary

Warning: TT: undefined function: 32PRE-LAB QUESTIONSAnswer the following questions and submit your group’s answer to the instructor. When you apply a 52 N force, a spring extends 13 cm. Assume the spring obeys Hooke’s Law. What is the spring constant (in N/m) for this spring? As above, when you appl...

Description

Laboratory Report

Foundation Physics 1

Experiment: Hooke’s Law PRE-LAB QUESTIONS Answer the following questions and submit your group’s answer to the instructor. 1.

When you apply a 52 N force, a spring extends 13 cm. Assume the spring obeys Hooke’s Law. What is the spring constant (in N/m) for this spring?

2.

As above, when you apply a 52 N force, a spring extends by 13 cm. How much energy was required to stretch the spring assuming you started from its unstretched length? How much energy (in Joules) must you use to stretch is another 13 cm (from 13 cm to 26 cm)?

3.

Suppose you have a mass m attached to a spring with constant k. The mass rests on a horizontal frictionless surface. Its equilibrium position is at x = 0. It is pulled aside a distance A and released. What is the speed of the mass as it passes the position x = A/2 (in terms of k, m, and A)? (Hint: Use conservation of energy)

1

Laboratory Report

Foundation Physics 1

INTRODUCTION For many “stretchy” materials, the amount of stretch is proportional to the stretching force (for fairly small stretches). In the Figure 1.1, part (b) shows a mass attached to a spring, at and in equilibrium. The spring has its natural length, and is not exerting any force on the mass. In part (a) the spring is stretched by an amount x, and is pulling on the mass with force Fs to the left. As the distance x is increased, the force Fs increases in proportion. This relationship is known as “Hooke’s Law”, and materials for which this is true are called “linear” materials. In this lab, you will measure the elastic properties of a linear device (a spiral metal spring) and a nonlinear device (an elastic band). Some springs (like the one in the figure) also allow for compression. In part (c) of the figure, the force is to the right, but still proportional to x, the amount of the compression.

Figure 1.1 OBJECTIVES a) To verify Hooke’s Law b) To determine the value of spring elasticity, k THEORY If a force F is exerted on a vertically suspended spring, the length of the spring changes an amount y from its initial length. Experiment shows that F is directly proportional to y. That is 𝐹 = 𝑘𝑦

(1.1)

where k is called the spring elasticity. The spring itself exerts a restoring force which returns the spring to its original length. This relation is known as Hooke’s law and is given by: 𝐹 = −𝑘𝑦

2

(1.2)

Laboratory Report

Foundation Physics 1

The minus sign in equation (1.2) shows that the restoring force is always in the opposite direction of the displacement. If the difference in applied force ∆𝐹 is given, the spring would then experience an elongation ∆𝑦 that can be written as in equation (1.3). 𝐹 = 𝑘∆𝑦

(1.3)

APPARATUS Stand with graduated scale, scale pan for masses, springs, and set of masses.

Figure 1.2 METHODOLOGY 1.

Set up the apparatus as shown in the Figure 1.2. Measure the length, yo of Spring A without the scale pan and masses.

2.

Weigh the mass of scale pan, mpan, and hooks it onto the spring. Measure the length, y1 of the spring.

3.

Add 25g mass, mmass into the scale pan. Measure the length, y2 of the spring.

4.

Repeat step 3 using a mass of 50g, 75g, 100g, 125g and 150g.

3

Laboratory Report

Foundation Physics 1

5.

Repeat the whole procedures to get the second reading then calculate the average reading.

6.

Using the same setup, repeat all the above steps using Spring B.

RESULT AND ANALYSIS Table 1.1

Mass, mmass (kg)

Total mass, (mpan+mmass) (kg)

Force, 𝐹 = 𝑚𝑔 (N)

Length of spring, y (m) yn

Reading 1

2

Average reading, 𝑦 𝑛

Elongation of spring, Δ𝑦 (m) Δ𝑦 =  𝑦𝑛 − 𝑦𝑜

yo y1 y2 y3 y4 y5 y6 y7

Table 1.2

Mass, mmass (kg)

Total mass, (mpan+mmass) (kg)

Force, ∆𝐹 = 𝑚𝑔 (N)

Length of Spring, y (m) yn

Reading 1

2

yo y1 y2 y3 4

Average reading,  𝑦𝑛

Elongation of spring, Δ𝑦 (m) Δy = y n − yo

Laboratory Report

Foundation Physics 1

y4 y5 Y6 Y7 ANALYSIS Plot a graph of force, 𝐹 versus elongation of spring, Δy for Spring A and B. Calculate the gradient of the graph and calculate all necessary error

DISCUSSION Discuss the results in relation to the objectives of the experiment.

CONCLUSION Based on the experiment that has been done, state your conclusion.

REFERENCES State all references here.

POST-LAB QUESTIONS 1. 2.

Spring B used in this experiment obeys Hooke’s law, determine the value of elongation, y of a spring if a total mass of 0.5 kg is attached to it? Show your calculation. Spring C consists of spring A and spring B that connected in series. Calculate the elongation of spring C if a 30 g mass was supported from the spring.

5...