PASCO ME-9502 Manuale utente

PASCO Mechanics

Statics System

ME-9502

Instruction Manual

012-12876B

*012-12876*

The cover page shows a a Friction Block on the Statics System Inclined Plane with a PASCO Mass Hanger from

the ME-8979 Mass and Hanger Set suspended by a thread over a Small Pulley. Most of the components of the

Statics System are held magnetically to the included workboard. This manual contains fifteen copy-ready experi-

ments about the fundamentals of statics.

iii

Table of Contents

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

Recommended Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Spares Package. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Components Package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

About the Manual. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

EXPERIMENTS

1. Hooke’s Law - Measuring Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2. Adding Forces - Resultants and Equilibriants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3. Resolving Forces - Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4. Torque - Parallel Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5A. Center of Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5B. Equilibrium of Physical Bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

6. Torque - Non-Parallel Forces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

7. The Inclined Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

8. Sliding Friction and Static Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

9. Simple Harmonic Motion - Mass on a Spring. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

10. Simple Harmonic Motion - The Simple Pendulum . . . . . . . . . . . . . . . . . . . . . . . . . . 53

11A: Simple Harmonic Motion - Physical Pendulum . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

11B: Minimum Period for a Physical Pendulum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

11C: Simple Harmonic Motion - Beam on a Spring . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

12. Simple Machines - The Lever . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

13. Simple Machines - The Inclined Plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

14. Simple Machines - The Pulley . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

15. Forces on a Boom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

Technical Support, Warranty, and Copyright. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

Statics System

iv 012-12876B

Statics System

ME-9502

Introduction

The study of mechanics often begins with Newton’s Laws of Motion. The first law describes the conditions for an

object to maintain its state of motion. If the net force on an object is zero, the acceleration of the object is zero.

The second law describes what happens if the net force on an object is not zero. The acceleration is directly pro-

portional to net force, in the same direction as the net force, and inversely proportional to mass, or

Much of what is studied in an introductory course deals with the ways that forces interact with physical bodies.

The PASCO Statics System is designed to help you investigate the nature of forces for the special case in which

there is no acceleration. In other words, the vector sum of all the forces acting on the body is zero.

One reason to study the case of no acceleration is because it is easier to measure non-accelerating systems than it

is to measure accelerating systems. A great deal can be learned about the vector nature of forces by studying the

many ways in which forces can be applied to an object without causing acceleration.The second reason is that in

our everyday experience, non-accelerated systems are the rule, not the exception.

Equipment

The ME-9502 Statics System consists of the Statics Board, Spares Package, Components Package, and Mass and

Hanger Set.

ME-9503 Statics Board

The Statics Board is a ferrous metal plate approximately

45 by 45 centimeters (18 by 18 inches) with a writable

white board finish on both sides.)

The board has rubber bumpers on its base. White board

pens (or “dry erase” pens) can be used to write and draw

directly on the board. The pens are available from statio-

nery stores and the ink can be erased with a cloth or a

white board eraser.

The Mounted Scale Assembly, Large and Small Pulley

Assemblies, Balance Arm Assembly, Force Wheel Assem-

bly, Torque Wheel Assembly, Inclined Plane Assembly,

and Utility Mount Assembly all attach magnetically to the

board. Components can be stored on the rear side of the

board when not in use. Except for the Inclined Plane

Assembly, all the components that can mount on the board

have a rubber ring on the base that protects the board and

the component. The round magnetic base is 6.5 centime-

ters (cm) in diameter.

If F0 then a = 0=

aFnet

----------

Statics Board

Statics System Equipment

2012-12876B

Important

When moving or removing any of

the magnetically mounted compo-

nents from the board, handle the

component by the magnetic base

rather than by the component itself.

This will reduce the strain on the

component.

A second board (available sepa-

rately) can be attached to the first

board with the three included con-

nector screws. To join the boards,

remove the connector screws from

the threaded holes on the side of

the first board. Put the edge of the

second board next to the first

board. Align the holes and join the

two boards with the connector

screws

Yes

Moving Components on the Board

Rear view of Statics Boards

Connector

screws

Use the Connector

screws to join two

Statics Boards together.

Model No. ME-9502 Recommended Equipment*

012-12876B 3

ME-9504 Spares Package

ME-9505 Components Package

ME-8979 Mass and Hanger Set

Components from the ME-8979 PASCO Mass and Hanger Set are used

in most of the statics experiments. The set includes four mass hangers,

a storage box, and twenty-seven masses ranging from 0.5 g to 100 g

made from brass, aluminum, or polycarbonate plastic.

Recommended Equipment*

Load Cell and Load Cell Amplifier

A PS-2201 5 N Load Cell can be used to measure force. When it is con-

nected through an amplifier to a PASCO interface or to a PASCO

hand-held data logger, the force data from the Load Cell can be

recorded, displayed, and analyzed.

*See the PASCO catalog or Web site at www.pasco.com for information about PASCO load cells, load cell

amplifiers, interfaces, hand-held data loggers, and data acquisition software.

Item Qty Item Qty

String Tie Assembly 3 Thumbscrew 6-32 by 5/8” (for Cord Clip) 2

Torque Indicator Assembly 6 Thumbscrew 4-40 by 1/2” (for balance arm protractor) 2

Nylon Thread, spool 1 Thumbscrew 6-32 by 1/4” (for balance arm pivot) 1

Cord Tensioning Clip 2 Washer 0.285” OD (for balance arm protractor) 2

Angle Indicator Arm 2 Plumb bob, brass (for inclined plane) 1

Item Qty Item Qty

Large Pulley Assembly 1 Utility Mount Assembly 1

Small Pulley Assembly 2 Mass Cart Assembly 1

Mounted Scale Assembly 1 Torque Wheel Assembly 1

Balance Arm Assembly 1 Inclined Plane Assembly 1

Force Wheel Assembly 1 Friction Block Assembly 1

Double Pulley Assembly 1 Asymmetrical Plate 1

ME-8979 Mass and Hanger Set

PS-2201 5 N Load Cell

Amplifier Model

Load Cell Amplifier (PASPORT) PS-2198

Dual Load Cell Amplifier PS-2205

Load Cell Amplifier (ScienceWorkshop) CI-6464

Statics System Spares Package (ME-9504)

4012-12876B

Stopwatch (ME-1234)

The PASCO Stopwatch has a liquid crystal dis-

play (LCD) with two display modes. Its precision

is 0.01 seconds up to 3599.99 seconds, and 1 sec-

ond up to 359999 seconds. Its memory holds up to

nine event times.

Mass Balance

Use a mass balance such as the OHAUS Scout

Pro Balance 2000 g (SE-8757A) or the OHAUS

Cent-O-Gram Balance (SE-8725).

Mounted Scale Assembly (ME-9824A)

The Mounted Scale Assembly (included in the ME-9505 Components Package) is also available separately as a

replacement or as an extra spring scale for experiments where measuring more than one force is required.

Spares Package (ME-9504)

The Spares Package contains some items which are used with assemblies from the Components Package. For

example, the String Tie Assembly snaps into the center of the Force Wheel Assembly and the Torque Indicator

Assembly snaps into the Torque Wheel Assembly. The Cord Tensioning Clip is used on the Utility Mount Assem-

bly. Other items such as the Angle Indicator Arms, thumbscrews, washers, and brass weight are replacement parts.

String Tie Assembly.

When the String Tie Assembly is snapped into the center of the Force

Wheel Assembly, you can use the apparatus to study force vectors. The

String Tie Assembly has two parts: a clear plastic inner part (the “force

disk”) that is free to move around in the center of the outer part, which

has a center hole and two tabs that snap into the Force Wheel Assembly.

(The two parts are not meant to be separated.)

Initial Setup

Get three threads that are 38 cm (15”) long. Put the threads through the

hole in the inner part of the String Tie Assembly. Tie the ends of the

threads together (for example, with an overhand knot) so that they cannot be pulled back through the inner part.

Torque Indicator Assembly

Note that the Torque Indicator Assembly has a

snap that can be connected to the Torque Wheel

Assembly. The other three assemblies are

spares.

Initial Setup

Tie a 30 cm (12”) thread to each of three Torque Indicator Assemblies.

Mass Balances

Stop Watch

Inner part

(force disk)

Outer part

Tab

Put

threads

through

this hole.

String Tie Assembly

Torque Indicator Assembly

Tie a

thread to

this hole. Snap connects

to Torque Wheel

Model No. ME-9502 Components Package (ME-9505)

012-12876B 5

Components Package (ME-9505)

Mounted Scale Assembly

The mounted scale has four strong magnets in its base. The tube is marked in

newtons (N), ounces (oz.) and millimeters (mm). The thumbnut allows the top

hook to be raised or lowered in order to align the red indicator disk with the

zero mark on the tube.

To zero the scale, mount the scale on the statics board. Leave the bottom hook

empty. Unscrew the thumbnut a few turns. Rotate the top hook clockwise

(left-to-right) to lower the indicator disk and counter-clockwise (right-to-left)

to raise the indicator disk. When the disk is aligned with the zero mark on the

tube label, tighten the thumbnut to hold the top hook in place.

To move the scale on the statics board, hold the scale by the tabs on the base

and push or pull the scale to the desired location. To remove the scale from the

statics board, lift one or both of the tabs on either side of the base away from

the board.

Large and Small Pulleys and Double Pulley Block

The Statics System comes with two Small Pulleys and one Large Pulley

mounted on magnetic bases. It also includes a Double Pulley Block (that does

not have a magnetic base). The Double Pulley Block is designed for

block-and-tackle experiments. A support thread can be tied to either end of the

Double Pulley Block.

All the pulleys have low friction ball bearings. The smaller pulleys are 2.41

cm (0.850”) outside diameter (OD) and 1.65 cm (0.650”) inside diameter (ID).

The larger pulleys are 2.79 cm (1.10”) OD and 2.28 cm (0.90”) ID.

Please use the tabs on the base of the components when moving them around or removing them from the statics

board.

Mass Cart and Friction Block

The Mass Cart and Friction Block are

designed to be used with the Inclined Plane

Assembly. The Mass Cart has low friction ball

bearings in each wheel and a metal rod in the

center for stacking extra masses. A thread can

be attached at either end.

The Friction Block is made of beech wood. It

has an “eye” hook at one end and is covered

with felt on the bottom and one side. Its dimensions are 2.54 cm by 5.08 cm by 6.35 cm (1.0” by 2.0” by 2.5”).

Spring

Indicator

disk

Scale

Base

Bottom

hook

Thumbnut

Top hook

Tab

Tube

Mounted Scale Assembly

Zero

mark

Small Pulley (2) Large Pulley Double Pulley Block

Mass Cart Friction Block

Felt Hook

Rod for

stacking

masses

Wood

Statics System Components Package (ME-9505)

6012-12876B

Inclined Plane Assembly

The Inclined Plane Assembly has four strong magnets on its back side that hold it in position on the Statics Board.

CAUTION: The magnets on the Inclined Plane Assembly are not covered with protective material.

Be careful to firmly hold the inclined plane when placing it on the board so that the magnets are

not damaged by “snapping” against the board.

The inclined plane has end stops at each end of the plane and a degree scale with a brass plumb bob for determin-

ing the angle of the incline.

Replacing the Plumb Bob

The ME-9504 Spares package includes a spare plumb bob (brass weight). To

replace the plumb bob, use a Phillips head (“crosshead”) screwdriver to loosen

the screw on the back of the degree scale. Remove the piece of thread and get a

new piece approximately 10 cm (4”) long. Put one end of the thread through the

hole in the brass weight and tie a double knot in that end of the thread so it will

not slip back through the hole. Put the other end of the thread through the small

hole near the top of the degree scale. Adjust the length of the thread so the plumb

bob can swing freely and then wind the end of the thread around the screw on the

back. Tighten the screw to hold the thread in place.

Inclined Plane Assembly

End stops

Plumb bob

Brass Weight

Putthread

through

the hole.

Tie a

knot.

Thread

Magnets

Indice

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