Question

Mechanics particle and tension help please?

A particle P of weight 20 N is suspended by two strings AP and BP. The tension in string AP is (ai + 8j ) and the tension in string BP is (6i+bj).

The value of a is _ and the value of b is __

The magnitude of the tension in string AP is __

The angle that string BP makes with the vertical is _

Give your answers as exact whole numbers or as decimals to 3 s.f.

Answer 1

See below.

Explanation:

Calling

`F_1 = (a,8)`
`F_2=(6,b)`
and
`P = (0,-m g)`

we have after equilibrium

`F_1+F_2+P = 0` or

`{(a+6=0),(8+b-m g=0):}`

solving for `a,b` gives

`a = -6`
`b = m g - 8`

now

`T_(AP) = sqrt(a^2+8^2) = sqrt(6^2+8^2)`
`T_(BP) = sqrt(6^2+b^2)= sqrt(6^2+(mg-8)^2)`

the anfle between `F_1, F_2` is obtaining by knowing

`<< F_1, F_2 >> = norm(F_1) norm(F_2) cos phi` then

`phi = arccos((<< F_1, F_2 >> )/(norm(F_1) norm(F_2))) = arccos((a xx 6 + 8 xx b)/(sqrt(a^2+8^2)sqrt(6^2+b^2)))`