Answer :
Answer:
F= 2.86KN
Explanation:
The attached diagram shows the motion of crate on a single line The forces acting on it have been resolved as shown in the attached figure.The kinetic friction opposes the motion.Now crate is moving with constant speed so the acceleration is constant.
Applying Newton's second law to determine the force F and also substituting the values for [tex]F_{k}[/tex] to eliminate normal force
[tex]$\sum_[/tex]F = ma
Now [tex]a_{x}[/tex] and [tex]a_{y}[/tex] components are zero
Horizontal and vertical forces are Force on crate, weight of crate and kinetic friction
[tex]$\sum F_{x} = Fcos\theta-f_{k}-mgsin\theta=0[/tex]
[tex]$\sum F_{y} = F_{n}- Fsin\theta-mgcos\theta=0[/tex]
therefore [tex]f_{k} = \mu_{k} F_{n}[/tex]
[tex]Fcos\theta- \mu_{k} F_{n}-mgsin\theta=0[/tex] >>> (1)
[tex]F_{n}=Fsin\theta+mgcos\theta[/tex]
By putting the above equation in equation 1 we get F
[tex]F=\frac{mg(sin\theta+\mu_{k}cos\theta) }{cos\theta-\mu_{k}sin\theta }[/tex]
By putting values we get
F = [tex]\frac{(80kg)(9.81\frac{m}{s^{2} })(sin36+(0.8)cos36) }{cos36-(0.8)sin36}[/tex]
F= 2860.8 N
F= 2.86KN
