A glider (mass = 0.12kg ) on a frictionless horizontal air track is connected by a light string over a pulley to a metal block (mass = 0.13kg ) hanging vertically (see figure below). The objects are released from rest and move 0.44 m .

a)Find the objects' acceleration.
b)Find the net work done on each.
c)Find the work done by the string on each.
d)Find the work done by gravity on the hanging mass.

To find the answers to the questions, we can use the principles of Newton's laws of motion and the concept of work. Let's go through each question step by step:

a) Find the objects' acceleration:
Using Newton's second law (F = ma), we can relate the force acting on the system to the acceleration of the objects. In this case, the force responsible for the acceleration is the tension in the string. Since the system is frictionless and neglecting the mass of the pulley, the tension force will be equal to the gravitational force on the hanging mass.

F = m * a

Tension = mg

By substituting the values of masses (mass of the block = 0.12 kg, mass of the glider = 0.13 kg, acceleration = a) and the acceleration due to gravity (g = 9.8 m/s^2), we can solve for the acceleration.

0.13 kg * a = 0.13 kg * 9.8 m/s^2

a = 9.8 m/s^2

Therefore, the objects' acceleration is 9.8 m/s^2.

b) Find the net work done on each:
The work done on an object is given by the formula W = Fd, where W is the work done, F is the force, and d is the displacement.

For the glider, there is no vertical displacement, only horizontal. As the glider moves horizontally, the tension force acts at an angle to the displacement, so the work done on the glider is zero.

For the hanging mass, the displacement is vertical. The net force acting on the hanging mass is the tension force pulling it upward, which is equal to its weight. Therefore, the net work done on the hanging mass can be calculated as:

Work = Force * displacement = weight of hanging mass * vertical displacement

Work = m * g * d = 0.13 kg * 9.8 m/s^2 * 0.44 m

By substituting the values, we can calculate the net work done on the hanging mass.

c) Find the work done by the string on each:
Since the glider is connected to the hanging mass by the string, the tension force in the string does work on both objects. The glider moves horizontally, while the hanging mass moves vertically.

The work done by the string on the glider can be calculated as:

Work = Force * displacement = Force * horizontal displacement

Since the tension in the string is the only horizontal force acting on the glider, the force exerted by the string is equal to the tension force. Therefore, we can calculate the work done by the string on the glider using the tension force and horizontal displacement.

The work done by the string on the hanging mass can be calculated similarly, using the tension force and the vertical displacement.

d) Find the work done by gravity on the hanging mass:
The work done by gravity on the hanging mass is equal to the change in its gravitational potential energy. As the hanging mass is pulled upward, its height increases, resulting in an increase in potential energy.

The work done by gravity can be calculated using the formula:

Work = m * g * h

Where m is the mass of the hanging mass, g is the acceleration due to gravity, and h is the increase in height.

By substituting the mass, acceleration due to gravity, and increase in height, we can calculate the work done by gravity on the hanging mass.