Question

a box is pushed down at an angle of 32 degrees on a rough surface. the box moves to the right. what equation should be used to find the net force in the y - direction? $f_{net,y}=f_n - f_g$ $f_{net,y}=f_p - f_f$ $f_{net,y}=f_n - f_g - f_pcos(32)$ $f_{net,y}=f_n - f_g - f_psin(32)$

Explanation:

Step1: Analyze vertical - direction forces

In the vertical direction, the forces acting on the box are the normal force $F_N$ acting upwards, the gravitational force $F_g$ acting downwards, and the vertical - component of the applied force $F_p$. The vertical component of the applied force $F_p$ is $F_p\sin(32^{\circ})$ (using trigonometry, where the vertical component of a vector at an angle $\theta$ with the horizontal is $F\sin\theta$) acting downwards.

Step2: Determine net - force formula

The net force in the y - direction $F_{net,y}$ is the sum of all the forces in the y - direction. Taking upwards as positive and downwards as negative, we have $F_{net,y}=F_N - F_g - F_p\sin(32^{\circ})$.

Answer:

$F_{net,y}=F_N - F_g - F_p\sin(32^{\circ})$