Physics Finding the Tension

Question

A 5-kg mass hangs at the end of a cord. Find the tension in the cord if the cord is accelerated at a) 1.7 m/s^2 up b) 1.3 m/s^2 down.

Answer 1

Let

m = 5 kg be the mass,

g = 9.8 m/s² be gravitational acceleration

If the string is accelerated up then the acceleration

adds to the gravitational acceleration (as if the object were heavier).

If the string is accelerated down then the acceleration

subtracts from the gravitational acceleration (as if the object were lighter).

Once we know the net acceleration, then tension can be calculated from

Newton's second law.

The reason is that in the case of mass on a cord, tension is force due

to the acceleration of the mass.

a) F = m(g + 1.7 m/s²)

= 5kg(9.8 m/s² + 1.7 m.s²) = 57.5N

b) F = m(g - 1.3 m/s²)

= 5kg(9.8 m/s² - 1.3 m.s²) = 42.5N