Answer:
The block has an acceleration of [tex]3 m/s^{2}[/tex]
Explanation:
By means of Newton's second law it can be determine the acceleration of the block.
[tex]\sum F_{r} = ma[/tex] (1)
Where [tex]\sum F_{r}[/tex] represents the net force, m is the mass and a is the acceleration.
[tex]F_{x} + F{y} = ma[/tex] (2)
The forces present in x are [tex]F = 10 N[/tex] and [tex]f = 4 N[/tex] (the friction force):
[tex]F_{x} = 10 N - 4 N[/tex]
Notice that [tex]f[/tex] subtracts to [tex]F[/tex] since it is at the opposite direction.
[tex]F_{x} = 6 N[/tex]
The forces present in y balance each other:
[tex]F_{y} = 0[/tex]
Therefore:
[tex]6 + 0 = ma[/tex]
[tex]6 N = (2kg)a[/tex] (3)
But [tex]1 N = 1 Kg.m/s^{2}[/tex] and writing (3) in terms of a it is get:
[tex]a = \frac{6 Kg.m/s^{2}}{2 Kg}[/tex]
[tex]a = 3 m/s^{2}[/tex]
So the block has an acceleration of [tex]a = 3 m/s^{2}[/tex].
Acceleration is the rate of change of motion. The acceleration of the block will be 3 m/s².
Acceleration can be defined as the rate of change of velocity of an object.
[tex]a =\dfrac{dv}{dt}[/tex]
Given to us
Mass of the block = 2 kg
Friction force on the block = 10 N
As the force, that is applied on the block will be resisted by the frictional force, but still, the block is moving with some acceleration towards the left,
[tex]F_x = F- F_{\mu}\\\\F_x = 10-4\\\\F_x = 6\ N[/tex]
We know that the force is given by the formula,
F = m x a
Substitute the value of the force,
[tex]6 = 2 \times a\\\\a = 3 m/s^2[/tex]
Hence, the acceleration of the block will be 3 m/s².
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