Happy Tuesday, friends Worldwide from Dr. TJ Gunn in Houston Texas USA…

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}) â€“ (5 kg)(5 m/s^{2})

T = 49 kg-m/s^{2} â€“ 25 kg-m/s^{2}

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