Question

Marcie shovels snow after a storm by exerting a force of 30.0 N on her shovelat an angle of 60.0° to the vertical. What are the horizontal and verticalcomponents of the force exerted by Marcie?

Answer 1

Given:

Force = 30.0 N

θ = 60 degrees to the vertical.

Let's find the horizontal and vertical components of the force exerted by Marcie.

Let's first sketch a free body diagram.

• Horizontal Component:

To find the horizontal component, apply the formula:

$\begin{gathered} sin\theta=\frac{F_x}{30} \\ \\ F_x=30sin60 \\ \\ F_x=25.98\text{ N} \end{gathered}$

Therefore, the horizontal component of the force is 25.98 N.

• Vertical Component:

To find the vertical component of the force, apply the formula:

$\begin{gathered} cos\theta=\frac{F_y}{30} \\ \\ F_y=30cos\theta \\ \\ F_y=30cos60 \\ \\ F_y=15\text{ N} \end{gathered}$

Therefore, the vertical component of the force is 15 N.

ANSWER:

• Horizontal component = 25.98 N

,

• Vertical component = 15 N