Question

A 40 N force applied at an angle of 37 degrees above the horizontal pulls a 5-kg box on a horizontal floor. The acceleration of the box is
3m=s2
. How large a fritional force must be retarding the motion of the box?

Answer 1

Answer on Question #40805 - Physics - Mechanics | Kinematics | Dynamics

A 40 N force applied at an angle of 37 degrees above the horizontal pulls a 5-kg box on a horizontal floor. The acceleration of the box is 3m=s2. How large a frictional force must be retarding the motion of the box?

Solution

We have, according the second Newton's law that the

$$m = 5 k g$$ $$a = 3 \frac {m}{s ^ {2}}$$ $$\alpha = 3 7 {}^ {\circ}$$ $$F = 4 0 N$$ $$m \ddot {a} = \vec {F} _ {r} + \vec {P} + m \ddot {g} + \vec {F}$$

Where $\vec{F}_r$ is frictional force, $\vec{P}$ is reaction force of floor, $m\ddot{g}$ is gravitational force, $\vec{F}$ is force applied at an angle of 37 degrees above the horizontal pulls

In term of projections, which are parallel to horizontal and vertical directions, we have

$$\left\{ \begin{array}{l} m a = F \cos \alpha - F _ {r} \\ m g - F \sin \alpha - P = 0 \end{array} \right. \Rightarrow$$ $$F _ {r} = F \cos \alpha - m a$$ $$F _ {r} = 1 6. 9 4 N$$

Answer:

$$F _ {r} = 1 6. 9 4 N$$