Acceleration of a Block on a Smooth Horizontal Surface

Given:
Force applied on the block = F
Angle of the force with the horizontal surface = 37°

To find:
Acceleration of the block

Assumptions:
1. The block is kept on a smooth horizontal surface, which implies that there is no friction between the block and the surface.
2. The mass of the block is known.

We can analyze the given situation using Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

bAcceleration = F / m

Where,
F is the force applied on the block
m is the mass of the block

Resolving the Applied Force

The force applied on the block can be resolved into its horizontal and vertical components using trigonometry.

The horizontal component of the force (Fh) can be calculated as:
Fh = F * cos37°

The vertical component of the force (Fv) can be calculated as:
Fv = F * sin37°

Acceleration of the Block

Since the block is on a smooth horizontal surface, there is no friction acting on it. Therefore, the horizontal component of the force (Fh) is the only force acting on the block in the horizontal direction.

Thus, the acceleration of the block (a) can be calculated as:
a = Fh / m

Substituting the value of Fh, we get:
a = (F * cos37°) / m

Calculating the Numerical Value

To calculate the numerical value of the acceleration, we need to know the values of the force (F) and the mass (m) of the block.

Once these values are known, we can plug them into the equation:
a = (F * cos37°) / m

After solving the equation, the resulting value will be the acceleration of the block.

Conclusion

The acceleration of the block on a smooth horizontal surface can be determined by resolving the applied force into its horizontal and vertical components. The block will only experience acceleration in the horizontal direction due to the absence of friction. By using Newton's second law of motion, we can calculate the acceleration by dividing the horizontal component of the force by the mass of the block.