Question

Two ropes are attached to a wagon, one horizontal to the west with a tension force of 30 N, and the other east and at an angle of 30° upward from horizontal with a tension force of 40 N. Find the components of the net force on the cart. Show your work.

Answer 1

`F_t=(4.64i+20j)N`

Step-by-step explanation:

Force in this problem is a vector quantity, so:

`x_1=F_1[cos(\theta_1)]\\y_1=F_1[sin(\theta_1)]`

and

`x_2=F_2[cos(\theta_2)]\\y_2=F_2[sin(\theta_2)]`

For this problem:

`F_1=30N\\F_2=40N`

`\theta_1=180`°=
`(pi)/(2)`

`\theta_2=30`°=
`(pi)/(6)`

The net force (
`F_t`) is equal to the sum of the forces:

`F_t=F_a+F_b\\\\F_a=30N[cos((\pi)/(2))i+sin((\pi)/(2))j]\\F_a=30N(-1i+0j)\\F_a=-30Ni\\\\F_b=40N[cos((\pi)/(6))i+sin((\pi)/(6))j]\\F_b=40N((\sqrt3)/(2)i+(1)/(2)j)\\F_b=(20\sqrt3i+20j)N\\F_b=(34.64i+20j)N\\\\F_t=[(-30i)+(34.64+20j)]N\\F_t=(4.64i+20j)N`

Hope that helps.