Question

A 1000-kg barge is being towed by means of two horizontal cables. One cable is pulling with a force of 80.0 N in a direction 30.0° west of north. In what direction should the second cable pull so that the barge will accelerate northward, if the force exerted by the cable is 120 N?

Answer 1

θ = 19.47°

Step-by-step explanation:

given,

mass of the barge = 1000 kg

force applied to pull = 80 N

direction = 30° west to north

force exerted by the cable = 120 N

direction = ?

first cable is pulling

in north direction = 80 cos ∅

= 80 cos 30°

= 69.28 N

in west direction = 80 sin ∅

= 80 sin 30°

= 40 N

the other cable will pull in the opposite direction of west

now,

`120 sin \theta = 40`

`sin \theta = (40)/(120)`

`\theta = sin^(-1){(1)/(3)}`

θ = 19.47°

the direction of the cable will be equal to θ = 19.47°