Respuesta :
Given:
Mass of couch, m = 23 kg
Angle = 32 degrees
Force = 120 N
Let's solve for the following.
A. Nomal force acting on the couch.
To find the normal force acting on the couch, apply the formula:
[tex]F_n=mg-F_y\sin \theta[/tex]Where:
m = 23kg
g = 9.81 m/s^2
Thus, we have:
[tex]\begin{gathered} F_n=23\ast9.81-120\sin 32 \\ \\ F_n=225.63-63.59 \\ \\ F_n=162.04\text{ N} \end{gathered}[/tex]Therefore, the normal force acting on the couch is 162.04 N
B. ACceleration of the couch.
To find the acceleration of the couch, apply the formula:
[tex]a_x=g\sin \theta[/tex]Thus, we have:
[tex]\begin{gathered} a_x=9.8\sin 32 \\ \\ \text{ a}_x=5.19m/s^2 \end{gathered}[/tex]Therefore, the accelertaion of the couch is 5.19 m/s^2
C. Let's find how hard he would have to pull on the couch at a 32 degrees angle to lift it off the ground.
To find the force, let's find the normal reaction.
The vertical component of his force is given by:
[tex]N=F\sin \theta[/tex]The component will need to counter the weight of the given couch before an additional force acts on the couch.
Thus, we have:
[tex]F\sin \theta=mg[/tex]Let's solve for F:
[tex]\begin{gathered} F=\frac{mg}{\text{sin}\theta} \\ \\ F=\frac{23\ast9.8}{\sin 32} \\ \\ F=\frac{225.4}{0.5299} \\ \\ F=425.3N \end{gathered}[/tex]Therefore, he will pull the couch with a force of 425.3 N.
This means that 120 N will not be enough to pull the couch.
ANSWER:
A. 162.04 N
B. 5.19 m/s²
C. 425.3 N
