Answer:
The tension in the string is 87.72 N.
Explanation:
Given that,
Mass of two each boxes = 10 kg
Suppose the inclined plane makes an angle is 60° with the horizontal and the coefficient of kinetic friction between the box and plane is 0.15.
We need to calculate the acceleration
Using balance equation
[tex]mg-T=ma[/tex]
Put the value into the formula
[tex]10g-T=10a[/tex]
[tex]98-T=10a[/tex]....(I)
Again using balance equation
[tex]T-mg\sin\theta-F_{f}=ma[/tex]
[tex]T-mg\sin\theta-\mu mg=ma[/tex]
Put the value into the formula
[tex]T-10g\sin60-\mu10\cos60=10a[/tex]
[tex]T-10\times9.8\dfrac{\sqrt{3}}{2}-0.15\times10\times9.8\cos\times\dfrac{1}{2}=10a[/tex]
[tex]T-84.8+7.35=10a[/tex]
[tex]T-77.45=10a[/tex]...(II)
From equation (I) and (II)
[tex]98-77.45=20a[/tex]
[tex]a=\dfrac{98-77.45}{20}[/tex]
[tex]a=1.0275\ m/s^2[/tex]
Put the value of acceleration in equation (I)
[tex]98-T=10\times1.028[/tex]
[tex]-T=10\times1.028-98[/tex]
[tex]T=87.72\ N[/tex]
Hence, The tension in the string is 87.72 N.
