Answer:
The acceleration of crate is [tex]8.35 \;\rm m/s^{2}[/tex].
Explanation:
Given data:
Mass of crate is, [tex]m=250 \;\rm kg[/tex].
Angle of inclination is, [tex]\theta = 30^{\circ}[/tex].
The coefficient of kinetic friction between crate and ramp is, [tex]\mu = 0.22[/tex].
Magnitude of horizontal force is, [tex]F=5000 \;\rm N[/tex].
In an inclined plane, the net force acting on the crate is given as,
[tex]F_{net}=Fcos\theta-(f+mgsin\theta)\\m a=Fcos\theta-(f+mgsin\theta)[/tex]
Here, a is the linear acceleration and g is the gravitational acceleration.
f is the frictional force in an inclined plane and its value is,
[tex]f=\mu \times N[/tex]
N is the normal reaction acting on crate in an inclined plane and its value is,
[tex]N=Fsin\theta+mgcos\theta\\N=5000 \times sin30+(250 \times 9.8 \times cos30)\\N=5000 \times sin30+(250 \times 9.8 \times cos30)\\N=4621.76 N[/tex]
Then frictional force is,
[tex]f=0.22 \times 4621.76=1016.78 \;\rm N[/tex]
Then acceleration is,
[tex]m a=Fcos\theta-(f+mgsin\theta)\\250 \times a=5000 \times cos30-(1016.78+250 \times 9.8 \times sin30)\\a=8.35 \;\rm m/s^{2}[/tex]
Thus, the acceleration of crate is [tex]8.35 \;\rm m/s^{2}[/tex].
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