Pulleys, Strings, Springs and Things Part 2

Chapter 6

Physics Springs

Blue Springs(Deland, FL)

Pulleys, continued…

Forces and PulleysFree-body Diagram

Mg

TF

T

Pulleys can get complex. The principle stays simple.

Example 6-7aAtwood’s Machine

Example 6-7bAtwood’s Machine

a a

T-m1g = a m2g - T = a

gmm

mma

ammgmgm

amTgm

amgmT

12

12

2112

22

11

)(

Simple Springs

xkF

Simple Spring Fling

L0

M

L

If the spring constant is K, free length is L0, what is L?

Here’s the free-body diagram:

F= -K(L-L0)

F= -Mg

Springy Thingy

Each spring produces a force according to F= -Kx. What is the force of two springs in “parallel”, for the same displacement x?

x

Force of Parallel Springs

1. Total force is –Kx, since each spring force remains the same.

2. Total force is ½ (-Kx), since each spring carries ½ the total weight.

3. Total force is 2(-Kx), since each spring exerts (-Kx).

Each spring produces force F=kx for displacement x. What is the force of two springs in parallel for displacement x?

Force of Springs in “Series”

F = -K1 x

F = -K1 x

x

x/2

x/2

What is the force of 2 springs in “series”, each with spring constant K, for same displacement x?

1. The force is just F = -K x, since each spring has the same force constant.

2. The force is twice as large.3. The force is half as big, F =

(1/2)(-K x)

Spring “Series”

F = -K1 x

F = -K1 x

x

x/2

x/2

F= -K x/2

F= -K x/2

F= -(K/2) x