a) See free-body diagram in attachment
b) The acceleration is [tex]2.46 m/s^2[/tex]
Explanation:
a)
The free-body diagram of an object is a diagram representing all the forces acting on the object. Each force is represented by a vector of length proportional to the magnitude of the force, pointing in the same direction as the force.
The free-body diagram for this object is shown in the figure in attachment.
There are three forces acting on the object:
- The weight of the object, labelled as [tex]mg[/tex] (where m is the mass of the object and g is the acceleration of gravity), acting downward
- The applied force, [tex]F_a[/tex], acting up along the plane
- The force of friction, [tex]F_f[/tex], acting down along the plane
b)
In order to find the acceleration of the object, we need to write the equation of the forces acting along the direction parallel to the incline. We have:
[tex]F_a - F_f - mg sin \theta = ma[/tex]
where:
[tex]F_a = 15 N[/tex] is the applied force, pushing forward
[tex]F_f = 5 N[/tex] is the frictional force, acting backward
[tex]mg sin \theta[/tex] is the component of the weight parallel to the incline, acting backward, where
m = 2 kg is the mass of the object
[tex]g=9.8 m/s^2[/tex] is the acceleration of gravity
[tex]\theta=15^{\circ}[/tex] is the angle between the horizontal and the incline (it is not given in the problem, so I assumed this value)
a is the acceleration
Solving for a, we find:
[tex]a=\frac{F_a - F_f - mg sin \theta}{m}=\frac{15-5-(2)(9.8)(sin 15^{\circ})}{2}=2.46 m/s^2[/tex]
Learn more about inclined planes:
brainly.com/question/5884009
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