find the work done ,if a weight of 25kg is lifted through a vertical height of 2m from the ground and it is raised to same place by pushing up an inclined plane making an angle of 30 degree with ground .neglect friction.

Physics

To find the work done when lifting the weight vertically and pushing it up an inclined plane, we'll break it down into two parts:

1. Lifting the weight vertically:
When lifting the weight vertically, the work done can be calculated using the formula:
Work = force × distance

The force required to lift the weight is equal to its weight, which can be calculated as:
Force = mass × gravity

Here, the mass of the weight is given as 25 kg and the acceleration due to gravity is approximately 9.8 m/s^2.

So, Force = 25 kg × 9.8 m/s^2 = 245 N

The distance lifted is given as 2 m.

Thus, the work done in lifting the weight vertically is:
Work = Force × distance = 245 N × 2 m = 490 Joules

2. Pushing the weight up an inclined plane:
To calculate the work done while pushing the weight up an inclined plane, we need to consider the component of the force acting parallel to the inclined plane.

The force acting parallel to the inclined plane can be calculated using the equation:
Force_parallel = Force × sin(angle)

Here, the angle of the inclined plane is 30 degrees, and the force acting is the same as the weight, which is 245 N.

So, Force_parallel = 245 N × sin(30 degrees) = 245 N × 0.5 = 122.5 N

The distance covered along the inclined plane is the same as the vertical height, i.e., 2 m.

Thus, the work done in pushing the weight up the inclined plane is:
Work = Force_parallel × distance = 122.5 N × 2 m = 245 Joules

So, the total work done in lifting the weight vertically and pushing it up the inclined plane is the sum of the work done in each part:
Total work done = Work (lifting vertically) + Work (pushing on inclined plane)
Total work done = 490 Joules + 245 Joules = 735 Joules