Question

A 225 kg block is pulled by two horizontal forces. The first force is 178 N at a 41.7-degree angle and the second is 259 N at a 108-degree angle. What is the x and y component of the total force acting on the block?

Answer 1

x: 52.9

y: 364.7

Step-by-step explanation:

Answer 2

52.9 N, 364.7 N

Step-by-step explanation:

First of all, we need to resolve both forces along the x- and y- direction. We have:

- Force A (178 N)

`A_x = (178 N)(cos 41.7^(\circ))=132.9 N\\A_y = (178 N)(sin 41.7^(\circ))=118.4 N`

- Force B (259 N)

`B_x = (259 N)(cos 108^(\circ))=-80.0 N\\B_y = (259 N)(sin 108^(\circ))=246.3 N`

So the x- and y- component of the total force acting on the block are:

`R_x = A_x + B_x = 132.9 N - 80.0 N =52.9 N\\R_y = A_y + B_y = 118.4 N +246.3 N = 364.7 N`