2nd Law: F, m, a Relationship
Unbalanced forces cause objects to accelerate:
Fnet = Resultant Force
Mass lifted upwards
T - mg = ma
T = m(g + a)
Mass accelerated downwards
T = m(g - a)
Two Masses Connected by a String
When two masses (A and B) are connected:
Top String (TA):
TA = mAg + mBg
Bottom String (TB):
TB = mBg
Conceptual Check
"Which cart is slowing down as it travels to the right?"
Check Your Understanding
5 quick questions — pick an answer to see if you’re right.
1. A 2.0 kg mass is lifted by a string with an upward acceleration of 0.2 m/s². Using g = 9.8 m/s², what is the tension?
2. A 2.0 kg mass hangs from a string and is accelerated downward at 1.8 m/s². Using g = 9.8 m/s², what is the tension?
3. Mass A (3.0 kg) hangs from a top string, and mass B (1.0 kg) hangs below A from a second string. At rest, what is the top string tension? (g = 9.8 m/s²)
4. In the same setup (A = 3.0 kg on top, B = 1.0 kg below, at rest), what is the bottom string tension? (g = 9.8 m/s²)
5. A mass hanging from a rope is accelerating upward. Compared with the mass's weight, the rope's tension is…