Final answer:
To make the box slide, a magnitude of horizontal pushing force greater than 176.4 N is needed to overcome the force of static friction.
Step-by-step explanation:
To calculate the magnitude of the horizontal pushing force needed to make the box slide, we need to consider the force of static friction between the box and the floor. The formula for static friction is given by fs = μsN, where fs is the force of static friction, μs is the coefficient of static friction, and N is the normal force. In this case, the normal force is equal to the weight of the box, which is given by N = mg. So, the force of static friction is fs = μs(mg).
In this example, the coefficient of static friction is 0.40, and the mass of the box is 45 kg. The force of static friction is therefore fs = 0.40(45 kg)(9.8 m/s²) = 176.4 N. This means that a pushing force greater than 176.4 N is needed to overcome the force of static friction and make the box slide.