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Two children pull on ropes attached to a tree, as shown below:

At what angle in degrees, measured clockwise from North, does the resultant force act? Give your answer to the nearest degree without units.

Two children pull on ropes attached to a tree as shown below At what angle in degrees measured clockwise from North does the resultant force act Give your answe class=


Answer :

onyebuchinnaji

The direction of the resultant force is 48⁰.

Horizontal and vertical component of each force

The horizontal component of the force is calculated as follows;

10 N is inclined to 35⁰ to the horizontal

Fx = 10 x cos(35)

Fx = 8.19 N

6 N is inclined to 70⁰ to the horizontal

Fx = 6 x cos(70)

Fx = 2.05 N

Sum of x component forces

∑Fx = 8.19 + 2.05

∑Fx =  10.24

Vertical component of the force

The vertical component of the force is calculated as follows;

10 N is inclined to 35⁰ to the horizontal

Fy = 10 x sin(35)

Fy = 5.74 N

6 N is inclined to 70⁰ to the horizontal

Fy = 6 x sin(70)

Fy = 5.64 N

Sum of y component forces

∑Fy = 5.74 N + 5.64 N

∑Fy =  11.38 N

Direction of the resultant force

θ = arc tan(ΣFy/ΣFx)

θ = arc tan(11.38/10.24)

θ =  48⁰

Thus, the direction of the resultant force is 48⁰.

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