Phys104 Lab > Labs > exp Forces Equilibrium

Objective

To study object in equilibrium

Introduction

When a rigid body is acted upon by a system of forces, a change may be produced in the linear (translational) velocity or in the angular (rotational) velocity of the body. Under certain conditions the body will be in equilibrium, that is, there will be no tendency for either its translational or rotational motion to change.

This investigation studies the conditions for objects in static equilibrium using Newton's first law. For translational equilibrium, the vector sum of all the forces acting on an object must be zero. For rotational equilibrium, the net torque acting on any axis must be zero.

This lab is divided in several experiments. You and your partner will be working individually on each experiment (obtaining separate data). You are required to do the Tension experiment and complete at least one of the other experiments. If possible do all three experiments. The individual experiments can be done in any order. When you have finished one experiment you can move onto another experiment that is not being worked on by your partner. Vectors and trigonometry is used in the analysis of this lab's data.

Tension Question: The Levi Straus trademark shows two horses trying to pull apart a pair of pants. Suppose Levi had only one horse and attached the other side of the pants to a fencepost. Using only one horse would: (a) cut the tension on the pants by one-half, (b) not change the tension on the pants at all, (c) double the tension on the pants?

Prelab

For the mass hang experiment and for the crane experiment: - draw the free-body diagram; - resolve each force/tension into x and y components

Pre-Lab Help: A proper free-body diagram shows the forces acting on a body, often considered at a single point. It is an abstraction ("free of any bodies") showing just the forces extending from a point (without showing pictures of the objects). Check your textbook as to how a free-body diagram is drawn.

- For the mass hang free-body diagram, show a single point indicating where the strings from the two scales and the hanging mass meet. Then show the forces extending from that point. Define angles with symbols on the diagram.

- For the crane free-body diagram, show a single point indicating where the meter stick, string from the scale and the hanging mass meet. Then show the three forces extending from that point that are from the hanging mass, the string tension and the tension in the meter stick. Define angles with symbols on the diagram.

- Also on the crane free-body diagram, show a fourth force due to the weight of the meter stick. This force acts in addition to the hanging mass and will be attributed to half of the meter stick mass ("half" as it divides evenly between the two end points from which the meter stick is held)

Resolving forces into xy components means writing equations for each force that look like F_x=... and F_y=... ( not ΣF_x=... and ΣF_y=... ) and using trigonometry to resolve each force by using its angle shown on the free-body diagram.

For translational equilibrium, one expects the sum of F_x forces to equal zero and the sum of F_y forces to equal zero.

Note: for this lab, it is strongly recommended that you bring your textbook.

Experiment: Mass on a string

A mass hanging between two strings has become a standard textbook problem for investigating the 1^st condition for equilibrium, the vector sum of all forces must be zero. This is usually done by resolving forces into their xy components at the center connection point and considering the x and y directions independently.

Setup the experiment as in the figure with a 500g mass. Arrange the mass such that the experiment is not symmetric (length and angle of string to each side is different).

Sketch the setup into your notes.
Use a protractor to measure all angles. From the spring balances, measure the tension in the strings.
Draw a free body diagram and include all your measurements.
From the measured forces and angles, determine the vertical components of the tension in the strings.
Compare the magnitudes the force due to the hanging mass to the total vertical force due to string tension. Compare by taking the absolute difference as well as a percent difference.
Write down a concluding sentence that compares expected to measured.
Repeat the experiment with a 700g mass on the string. Just take the measurements for this and leave the calculations for a future time.

Experiment: Crane

Using a line to extend a beam from a post is an equilibrium problem with a number of examples in real life such as a hanging bridge, construction cranes, hanging neon signs.

Setup the experiment as in the figure with a 200g hanging mass. Change the string length and position the clamp on the upright pipe such that the ruler (beam) is level. You should have a unique setup from your partner.

Sketch the setup into your notes and measure/record all angles. Read the scale with the 200g mass. Also measure the mass of a sample wooden meter stick.
Draw a free body diagram and include all your measurements. Note, the meter stick mass adds into the vertical forces by distributing it mass equally between the two end points.
Determine the tension in the meter stick from the measured angles and the measured tension in the string
Determine the vertical component of the tension in the string. Compare the magnitudes of this force component to the force due to the hanging mass and the meter stick by writing a statement using percent difference.
Repeat the experiment with a 300g mass (ensure the beam/ruler is horizontal). Just take the measurements for this and leave the calculations for a future time.

Notice the similarity of this experiment to cranes used in construction.

Experiment: Tension, an internal force

Introduction
An internal force arise in response to external forces acting on a body.
This is similar to normal or friction forces which also only arise due to the action of some other force.

Internal forces are characterized as

tension: arises from stretching or pulling apart, often associated with a string, cable or chain but also occurs in rigid bodies such as pulling a meter stick from both ends
compression: from pushing or squeezing on a rigid body, opposite of tension
shear: from two external forces offset, not directly opposite each other
bending
torsion: twisting

The internal forces relate to

stress (force per unit area, useful was to characterize internal force)
strain (effect of force as size deformation relative to original)
creep (effect of force as permanent deformation due to stress)
modulus (property of material, ratio of stress to strain, measures resistance to stress)

In this lab we are looking at tension (such as a string pulled) and compression (such as a meter stick pushed from opposite ends). For tension or compression, the internal force is along the axis of the body (based on two external forces acting) and is not given a direction except when it acts on the external force. Tension or compression internal force has a magnitude equal to the acting external force.

Tension Experiment
For this lab exercise, we are looking at tension (in a string or an elastic). The exercise could equally apply to compression (or shear, bending, torsion for that matter).

When you pull on a rope attached to a crate, your pull is somehow transmitted down the rope to the crate. Tension is the name given to forces transmitted in this way along strings, ropes, rubber bands, springs and wires. Note that (obviously) the rope by itself is unable to exert a force on the crate if your are not pulling on the other end. Thus tension forces are passive, they only act in response to an active force like your pull.

If you apply a force to the end of a rope as in the picture above, is the whole force transmitted to the crate, or is the force at the crate smaller or larger than your pull?
If the rope is longer, will the force applied to the crate be larger, smaller or the same as with the shorter rope? Does it matter how long the rope is?
Suppose that instead of a rope, you used a bungee cord or large rubber band. Will the force applied to the crate be larger, smaller or the same as with the rope? Suppose that you use a strong wire cable?
How is the force "magically" transmitted along the rope?

As in the figure, attach a rubber band between two spring scales. Without pulling, notice if there is a difference in readings between the scales. Now pull on one scale and observe the difference in readings between the two scales.

Base on your readings of the scales, is the force transmitted down to the other end when you pull on one end of the rubber band? Explain.
As you increase the force applied to the rubber band, what happens to the length of the rubber band? Propose a mechanism based on these observations to explain how the force is transmitted down the rubber band from one scale to the other.
Indicate on a diagram the directions of the forces exerted by the rubber band on to the scales.

Replace the rubber band with short piece of string with loops at both ends and repeat the experiment. Now do the same for a longer piece of string.

Based on the readings of the scales, when you pull on one end of the string, is the force transmitted undiminished down to the other end? Does it matter how long the string is? Explain.
Did the string stretch at all when you pulled on it? Can you propose a mechanism for the transmission of the force along the string?

Setup a scale with a 1000g mass over a pulley as shown in the picture. Vary the angle the scale/string makes with the pulley and observe the scale reading.