1. A 10-kg object is dropped from rest. After falling a distance of 50 m, it has a speed of 26 m/s.

a. Write the expression for the change in mechanical energy caused by the dissipative (air) resistive force on the object during this descent.
b. Calculate the energy.

a = drop in potential energy = m g h

b = gain in kinetic energy = (1/2) m v^2

work done by friction = a - b

-1.5kj

a. The expression for the change in mechanical energy caused by the dissipative (air) resistive force can be given by the work-energy principle, which states that the work done on an object is equal to the change in its mechanical energy.

The work done by the dissipative force can be calculated using the equation:

Work = Force x Distance

In this case, the force is the air resistive force and the distance is the distance the object has fallen. The air resistive force is opposite to the direction of motion, so the work done by the air resistive force is negative.

Therefore, the expression for the change in mechanical energy caused by the air resistive force is:

Change in Mechanical Energy = -Work = - (force x distance)

b. To calculate the energy, we need to know the value of the air resistive force. However, the given information does not provide us with the necessary information to calculate it. So, we cannot calculate the energy with the given information.

a. To find the expression for the change in mechanical energy caused by the dissipative (air) resistive force on the object, we need to consider the work done by this force. The work-energy principle states that the work done on an object equals the change in its mechanical energy.

The expression for work is given by:

Work = Force * Distance * cos(theta)

In this case, the force is the air resistive force, the distance is the descent distance (50 m), and theta is the angle between the force and the direction of motion (which we'll assume is 0 degrees, so cos(theta) = 1).

Let's assume that the air resistive force is proportional to the square of the speed of the object. So, the air resistive force can be expressed as:

F_air = k * v^2

where k is a constant.

Therefore, the expression for the work done by the air resistive force is:

Work_air = (k * v^2) * d

where v is the final speed (26 m/s) and d is the descent distance (50 m).

b. To calculate the energy dissipated by the air resistive force, we need to know the value of the constant k. Unfortunately, the question does not provide that information, so we cannot give a specific numerical answer. However, once you have the value of k, you can substitute it into the expression for the work (from part a) and calculate the energy dissipated.