# 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/s^{2}

m = mass, kg

g = gravitational force, 9.8 m/s^{2}

a = acceleration, m/s^{2}

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/s^{2}) + (5 kg)(0)

T = 49 kg^{-m}/s^{2} = 49 N

2) Now assume an acceleration of + 5 m/s^{2} upwards.

T = mg + ma

T = (5 kg) (9.8 m/s^{2}) + (5 kg)(5 m/s^{2})

T = 49 kg^{-m}/s^{2} + 25 kg^{-m}/s^{2}

T = 74 kg^{-m}/s^{2} = 74 N

3) Now assume a downwards acceleration of a = -5m/s^{2}

T = mg + ma

T= (5 kg) (9.8 m/s^{2}) - (5 kg)(5 m/s^{2})

T = 49 kg-m/s^{2} - 25 kg-m/s^{2}

T = 24 kg-m/s^{2} = 24 N

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