Tension Formula
The tension on an object is equal to the mass of the object x gravitational force plus/minus the mass x acceleration.
T = mg + ma
T = tension, N, kg-m/s2
m = mass, kg
g = gravitational force, 9.8 m/s2
a = acceleration, m/s2
Tension Formula Questions:
1) There is a 5 kg mass hanging from a rope. What is the tension in the rope if the acceleration of the mass is zero?
Answer: The mass, m = 5 kg; the acceleration, a = 0; and g is defined.
T = mg + ma
T= (5 kg) (9.8 m/s2) + (5 kg)(0)
T = 49 kg-m/s2 = 49 N
2) Now assume an acceleration of + 5 m/s2 upwards.
T = mg + ma
T = (5 kg) (9.8 m/s2) + (5 kg)(5 m/s2)
T = 49 kg-m/s2 + 25 kg-m/s2
T = 74 kg-m/s2 = 74 N
3) Now assume a downwards acceleration of a = -5m/s2
T = mg + ma
T= (5 kg) (9.8 m/s2) - (5 kg)(5 m/s2)
T = 49 kg-m/s2 - 25 kg-m/s2
T = 24 kg-m/s2 = 24 N
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