An Introduction to Statics

Unit 3, Presentation 4

What is Statics?

Statics: The study of the forces associated with objects at equilibrium with each other.

No motion with objects in equilibrium

All accelerations are equal to 0

All net forces are equal to 0

Statics Example ProblemA traffic light of mass 50 kg hangs from a vertical cable tied to two other cables that are fastened to a support (see below). The upper cables make angles of 37.0° and 53.0° with the horizontal. Find the tension in each of the three cables.

37.0° 53.0°

T1 T2

T3

Statics Example Problem Cntd.Consider drawing free body diagrams for two objects: the stop light and the knot connecting the three cables.

FBD for the Stop Light FBD for the knot

mg

T3

T3

T2T1

NmgT

mamgT

490)8.9(50

0

3

3

Must break down vectors T1 and T2 into x and y components.

Statics Example Problem Cntd.

T1

37.0°

T1x

T1y

0.37cos11 TT x

0.37sin11 TT y

T2

T2x

T2y

0.53cos22 TT x

53.0°

0.53sin22 TT y

Statics Example Problem Cntd.

x-direction y-direction

037cos53cos 12 TT

NTT

mgTT

mgTT

490)8.9(5037sin53sin

37sin53sin

037sin53sin

12

12

12

Note: Two equations, two unknowns…solve a system of linear equations.

We’ll use substitution.

11

2 33.153cos

37cosT

TT

NNTT

NT

T

TT

TT

392)295(33.133.1

295

49066.1

49060.006.1

49037sin)53(sin33.1

12

1

1

11

11

Another Statics Example Problem

A sled is tied to a tree on a frictionless, snow-covered hill, as shown below. If the sled weighs 77.0 N, find the force exerted by the rope on the sled and the magnitude of the normal force exerted by the hill on the sled.

30.0°

mg

Fn T

Another Statics Example Problem

x-direction y-direction

NT

mgT

mgT

5.38)30(sin77

sin

0sin

sin

0cos

mgF

mgF

N

N

0.30

0.77

?

?

Nmg

F

T

N NFN 7.66)30(cos77