A student pulls a box of books on a smooth horizontal floor with a force of 100 N in a direction of 37° above the horizontal. If the mass of the box and the books is 40.0 kg, what is the acceleration of the box?

1.9965 m/s²

Explanation:

Acceleration: This can be defined as the rate of change of velocity. The S. I unit of acceleration is m/s².

From the question,

F' = ma ... Equation 1

Where F' = horizontal force, m = mass of the box, a = acceleration of the box.

But,

F' = FcosФ ... Equation 2

Where F = Force applied to the box, Ф = angle of between the force and the horizontal.

Substitute equation 2 into equation 1

FcosФ = ma

make a the subject of the equation

a = FcosФ/m ... Equation 3

Given: F = 100 N. Ф = 37°, m = 40 kg.

Substitute into equation 3

a = 100 (cos37°) / 40

a = 100 (0.7986) / 40

a = 79.86/40

a = 1.9965 m/s²