4 a)iiiiii 4. (a) A box of mass, m, slides down an inclined plane that makes an angle 0 withthe horizontal as shown in Figure 1. Find a differential equation for thevelocity v(t) of the box at time t in each of the following three cases:i. No sliding friction and no air resistance.ii. With sliding friction and no air resistance.iii. With sliding friction and air resistance.In cases (ii) and (iii), use the fact that the force of friction opposing themotion of the box is µN, where u is the coefficient of sliding frictionand N is the normal component of the weight of the box. In case (iii)assume that air resistance is proportional to the instantaneous velocity.frictionmotion-W = mg |50Figure 1: Question 4(b) In part (a), suppose that the box weighs 412 kg.m/s², acceleration due togravity is taken to be 9.81 m/s², the angle of inclination of the plane is0 = 30, the coefficient of sliding friction is µ = v3/4, and the additionalretarding force due to air resistance is numerically equal to u. Solve thedifferential equation in each of the three cases, assuming that the box startsat rest from the highest point 50 metres above ground.

Name: 4 a)iiiiii 4. (a) A box of mass, m, slides down an inclined plane that
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Description: 4 a)iiiiii 4. (a) A box of mass, m, slides down an inclined plane that makes an angle 0 withthe horizontal as shown in Figure 1. Find a differential equation for thevelocity v(t) of the box at time t in each of the following three cases:i. No sliding