Question

Three dogs are fighting over a bone. One is pulling to the left with a force of 20N, another

to the right with a force of 35N and the third upward with a force of 15N. What is the net
force on the bone? This is a multiple-select problem: You must select a magnitude for the
force and an angle for the force.

Answer 1

Net force = 21.12 N

angle for the force α = 45°

Step-by-step explanation:

In this problem, we will take the left as the negative x-axis, the right as the positive x-axis, and the upward direction as the positive y-axis.

The 20 N force to the left has an x component of -20 N, and y component of 0 N

The 35 N force to the right has a x component of 35 N, and a y component of 0 N

The 15 N upwards has an x component of 0 N, and a y component of 15 N

We resolve the forces into the x and y components.

for the x component Fx

Fx = -20 + 35 + 0 = 15 N

For the y component Fy

Fy = 0 + 0 + 15 = 15 N

Net force Fn =
`\sqrt{Fx^(2) + Fy^(2) }`

`Fn = \sqrt{(15)^(2) + (15^(2) ) }`

Net force Fn = 21.21 N

for the angle,

`tan\alpha = (Fy)/(Fx) = (15)/(15)`

`tan\alpha = 1`

α =
`tan^(-1)` 1

angle for force α = 45°