A man is holding a suitcase as shown in the figure. Using the mentioned data in the figure calculate the magnitude & direction of the suitcase’s acceleration.

Solution:

To calculate the magnitude and direction of the suitcase's acceleration, we need to use the following formula:

`F_net = ma`

where `F_net` is the net force acting on the suitcase, m is the mass of the suitcase, and a is its acceleration.

In this scenario, the suitcase is held in place by the man's hand, so it is not moving. Therefore, its acceleration is zero. However, there are two forces acting on the suitcase: the force of the man's hand holding it up (F), and the force of gravity pulling it down (mg).

To calculate the net force, we need to subtract the force of gravity from the force exerted by the man's hand:

`F_net = F - mg`

`F_net = 168 N - 166.6 N = 1.4 N`

Now we can use the formula above to solve for the acceleration:

`a = F_net / m`

`a = {1.4 N} / {17 kg}`

`a = 0.0824 m/s^2`

Therefore, the magnitude of the suitcase's acceleration is 0.0824 m/`s^2`. Since the suitcase is not moving, its acceleration is in the direction opposite to the force of gravity, which is upwards. Therefore, the direction of the suitcase's acceleration is upward.