Question

Imagine you are holding a box in your hand, the force required for you to hold the box with mass 4.54kg and you want to accelerate the box 2m/s2. Move the box in your hand a) upward vertically, b) downward vertically, and c) horizontally. Calculate the magnitudes of forces in the x and y direction.

Answer 1

(a) Fₓ = 0 N

`F_y` = 9.08 N

(b)

(a) Fₓ = 0 N

`F_y` = 9.08 N

(c)
`F_y` = 0 N

Fₓ = 9.08 N

Step-by-step explanation:

The magnitude of the force will remain the same in each case, which is given as follows:

F = ma (Newton's Second Law)

where,

F = force = ?

m = mass = 4.54 kg

a = acceleration = 2 m/s²

Therefore,

F = (4.54 kg)(2 m/s²)

F = 9.08 N

Now, we come to each scenario:

(a)

Since the motion is in the vertical direction. Therefore the magnitude of the force in x-direction will be zero:

Fₓ = 0 N

For upward direction the force will be positive:

`F_y` = 9.08 N

(b)

Since the motion is in the vertical direction. Therefore the magnitude of the force in x-direction will be zero:

Fₓ = 0 N

For upward direction the force will be negative:

`F_y` = - 9.08 N

(c)

Since the motion is in the horizontal direction. Therefore the magnitude of the force in y-direction will be zero:

`F_y` = 0 N

Fₓ = 9.08 N