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
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"Which cart is slowing down as it travels to the right?" |
Choice 2
Check out this
Video at Georgia Pacific Broadcasting
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