Question

1) Up until now we have always ignored air resistance. We should now add it. Let us just think of simple 1-dimensional problem, dropping a ball of mass m from a height H but 2 with air resistance. We can model the air resistance as a force proportional to the velocity, fair = bv. The coefficient bis a constant. (For this problem you can use calculus textbooks or wolfram alpha to do the calculus.) What are the units on b? Why does it make sense for the force to be dependent on the velocity? The constant b depends on other physical parameters, can you think of what these might be? I only gave the magnitude of the air resistance force. What is the direction? Choose a standard coordinate system with the 3 direction being vertical and positive up. Write out Newton's second law for this problem. Since this is a 1-dimensional problem you don't have to worry about vector notation. When we derived our kinematic equations we integrated Newton's second law, essen- tially solving for the velocity and position from a known function for the acceleration. The kinematic equations assumed what abut the acceleration? How is this problem different? When the air resistance force and gravitational force balance out the acceleration goes to zero. When the acceleration goes to zero there is no longer a change in motion, hence the velocity does not change (right?). When this happens we say the object has reached terminal velocity, vy. Find an expression for the terminal velocity given the parameters of the problem. Following the procedure similar to the constant acceleration case, find the velocity as a function of time by integrating F = ma. Plot this function. Integrate your velocity v = dy/dt to get y as a function of time. Plot this function.
please explain the answer.

Answer 1

Since as per HOMEWORKLIB RULES we can only answer 4 subparts of the question hence answering first 4 sub parts of the question.

1)

Since f = bv

f has units of Force i.e. Netwon

v has units of velocity i.e. m/s thus b has units of Ns/m

also since N can also be written as kgm/s²

thus the units of b can also be written as kg/s.

2)

Since the drag force is caused due to the relative friction between two objects (mass and air in this case) thus there is resistance developed between mass and air. As the objects keep moving in the air, it tries and displace more and more air thus with increasing speed, object is trying to move more air thus causing more air drag over it.

Yes the constant b should also depend on the shape and size of the object.

3)

Since the air drag is always in the direction opposite to the motion of the body thus the air drag force will be acting upwards as the object is moving downwards.

4)

Air drag force will be acting upwards on the mass.

Weight of the object will be acting downwards on the mass.

Let the net acceleration of the object be a.

therefore as per newton's second law

mg - F = ma