4.1 A car of mass M travels in a straight line at constant speed along a level road with a coefficient of friction between the tires and the road of \(\mu\) and a drag force of \(D\). The magnitude of the net force on the car is a) \(\mu M g\). c) \(\sqrt{(\mu M g)^{2}+D^{2}}\) b) \(\mu M g+D\)

The friction force between the tires and the road can be determined using the formula: \(F_{friction} = \mu M g\), where \(M\) is the mass of the car, \(g\) is the gravitational acceleration, and \(\mu\) is the coefficient of friction.

Since the car is moving at a constant speed, the net force acting on it is zero. Thus, the friction force and drag force must be equal but opposite in direction. Mathematically, this can be represented as: \(F_{friction} = D\), which implies \(\mu M g = D\).

We will test each of the given formula options to check if it represents the net force as zero: a) \(\mu M g\): This option represents the friction force and not the net force. So, this is incorrect. b) \(\mu M g + D\): Since the friction force and drag force are equal and opposite, their sum should be zero. But this option represents their sum which cannot be equal to zero since both forces are nonzero. So, this is incorrect. c) \(\sqrt{(\mu M g)^{2}+D^{2}}\): The net force on the car is given by the vector sum of the friction force and the drag force. Since they are equal and opposite in direction, their sum is equal to zero. Using the Pythagorean theorem, we can find the net force as \(\sqrt{(\mu M g)^2 + (-D)^2} = \sqrt{D^2 +D^2} = \sqrt{2D^2}\). This option represents the magnitude of the net force, which should be equal to zero. So, this option is also incorrect. Based on these tests, none of the given formula options represent the net force on the car correctly.