Free falling body

1. Simulate and plot a freefalling body (point mass) of mass 1 kg and inertial properties 1 kgm2 in the y-axis (gravity should be -9.81 m/s2 in the negative y-direction) (Use dimension of length in meters not mm) [60]

Ans-

Mass And Inertia Properties

Changing of units to meters

Gravity

Displacement Vs Time

1. Does the mass and inertial properties of the body depend on the rate of fall? Justify your answer with analytical(with equation) and simulation results. [20]

Ans- Rate of fall of a free body is completely independent of the mass and inertial properties of the body. Assuming the body is falling freely in vaccum. The only force acting on it is the weight of the body.

F = W = m*g

According to the Newton’s Second law of motion,

F = m*a

a = F/m

a = W/m = mg/m

a = g

Thus mass of the body does not affect the gravity of free falling object. Inertia is based on the mass of the object. Since gravity doesn\'t change the mass of the object, neither does it change the inertia.

Simulation Results:-

For Mass and Inertia of 1 kg and 1kgm2 (top right), 50 kg and 50 kgm2 (bottom left) and 100 kg and 100 kgm2 (bottom right)

All the Graphs are same for different mass and inertia.

1. In what case will the mass have an effect on the rate of fall? In the same case what other physical characteristics will affect the rate of fall? [20]

Ans- We have seen that in vaccum the mass does not affect the the gravity on free falling body. However if we take air resistance into account, then drag comes into play.

W = constant = mg

Drag = (C_d *r*V²*A)/2

Therefore motion is given by,

F=m*a

a = F/m = (W - D)/m

As drag increases, rate of falling decreases. Drag is directly related to surface area of the object. More the surface area more is the drag and vice versa. Thus rate of falling depends on its mass, surface area and the acceleration due to gravity.