2nd Law - Relationship between F, m, a

 

 

 

Unbalanced forces
cause objects to accelerate:

 

 

ΣFnet = ma

Fnet = Resultant

 

 

 

Ex) Mass M below is lifted up with an acceleration a. Find the tension in the string T

ΣFnet = ma

 

 

(up positive)

 

 

T - mg = ma

 

T = ma + mg

 

String Pulled up

 

T = m(g + a)

 

 

String Acelerated down?

 

 

T = m(g - a)

Two masses are connected by a string.

Find tension force on top and bottom rope.

 

 

Ex 1) Two masses are connected by a string and remain at rest.

Find tension force on top and bottom rope.

SF = 0

Top String Tension Force

 

TA - mag - mbg = 0

 

TA = mag + mbg

 

Bottom String Tension Force

 

TB - mbg = 0

TB = mBg

Ex 2) Find the tension of top and bottom string if objects accelerated upward

 

Free body diagram B (easier)

Sketch all forces on A

Force of tension on B (easier)

Free body diagram B

Sketch all forces on B

 

 

 

 

 

 

SF = mBa

TB - mBg = mBa

 

TB = mBa + mBg

= (force of accel. of B + weight of B)

 

 

Sketch all forces on A

 

 

 

 

 

SF = mAa

TA - TB - mAg = mAa

 

TA = mAa + mAg + TB

 

Since TB = mBa + mBg

TA = mAa + mAg +mBa+mBg)

 

 

TA=(mAa+mBa)+(mBg+mAg)

= (force of accel) + (weights)

 

 

Giancoli p. 98) 8, 25

 

 

 

 

 

"Which cart is slowing

down as it travels to

 the right?"

Jan 2006

 

 

 

 

Choice 2

 

 

 

Check out this

Video at Georgia Pacific Broadcasting

 

 

 

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