You want to use a rope to pull a 10-kg box of books up a plane inclined 30∘ above the horizontal. The coefficient of kinetic friction is 0.29. The rope pulls parallel to the incline.
What force do you need to exert on the rope if you want to pull the box with a constant acceleration of 0.50 m/s2 up the plane?

Newtons second law of motion shows the relation between the force mass and acceleration of a body. It says, that the force applied on the body is equal to the product of mass of the body and the acceleration of it.

It can be given as,

[tex]F=ma[/tex]

Here, (m) is the mass of the body and (a) is the acceleration.

Given information-

The mass of the box of books is 10 kg.

The inclination of the plane is 30 degrees above the horizontal.

The coefficient of kinetic friction is 0.29.

The constant acceleration of box is 0.50 m/s2.

The total force acting on the box of mass is,

1) Normal force acting on the body, perpendicular to the inclined surface due to the application of gravitational force. This force is the product of mass times the gravitation. Thus,

[tex]F_n=10(9.8)\cos(30)[/tex]

[tex]F_n=84.87[/tex]

2) Frictional force in the opposite direction of the force applied on the body. This force is equal to the product of normal force and the coefficient of kinetic friction is 0.29.

[tex]F_f=84.87(0.29)[/tex]

[tex]F_f=24.16[/tex]

3) The force which is parallel to the inclined plane and trying to accelerate the block is,

F_y=10(9.8)\sin(30)

[tex]F_y=49[/tex]

The force need to exert on the rope if you want to pull the box with a constant acceleration of 0.50 m/s2 up the plane is equal to the sum of mass time acceleration, friction force which is opposing it and the parallel force.

Thus,

[tex]F=10(0.5)+24.61+49[/tex]

[tex]F=78.61[/tex]

Thus, the force need to exert on the rope if you want to pull the box with a constant acceleration of 0.50 m/s2 up the plane is 78.61 N.

Learn more about the second law of motion here;

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