A 5 kg block is pulled along a horizontal frictionless floor by a string and exerts force of magnitude 16 N at an angle 30 degree.What is the magnitude of the acc of block?
To find the magnitude of the acceleration of the block, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration.
First, we need to resolve the force acting on the block into its horizontal and vertical components. The force of 16 N at an angle of 30 degrees can be split into two components: the horizontal force and the vertical force.
The horizontal component (F_horizontal) can be found by multiplying the magnitude of the force (16 N) by the cosine of the angle (30 degrees):
F_horizontal = 16 N * cos(30 degrees)
F_horizontal = 16 N * 0.866
F_horizontal = 13.86 N (rounded to two decimal places)
The vertical component (F_vertical) can be found by multiplying the magnitude of the force (16 N) by the sine of the angle (30 degrees):
F_vertical = 16 N * sin(30 degrees)
F_vertical = 16 N * 0.5
F_vertical = 8 N
Since there is no vertical force acting on the block (frictionless floor), the vertical component of the force does not affect the magnitude of the acceleration of the block. Therefore, we can ignore the vertical component in this case.
Now, we can use Newton's second law to find the magnitude of the acceleration (a). Rearranging the equation, we have:
F_horizontal = m * a
where F_horizontal is the horizontal component of the force, m is the mass of the block, and a is the acceleration.
Substituting the values we found:
13.86 N = 5 kg * a
Solving for a:
a = 13.86 N / 5 kg
a = 2.77 m/s^2 (rounded to two decimal places)
The magnitude of the acceleration of the block is 2.77 m/s^2.