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A body of mass 2kg is pulled up along a smooth inclined plane of length 4 m angle 30⁰ . find the work done?

To determine the work done in pulling a body up an inclined plane, we need to consider the forces acting on the body and the distance moved along the incline. In this case, we have a body of mass 2 kg being pulled up a smooth inclined plane that is 4 meters long, with an angle of 30 degrees. Let's break this down step by step.

Understanding the Forces Involved

When a body is pulled up an incline, the primary force we need to consider is the gravitational force acting on the body. The weight of the body can be calculated using the formula:

• Weight (W) = mass (m) × gravitational acceleration (g)

Here, the gravitational acceleration (g) is approximately 9.81 m/s². For our body:

• W = 2 kg × 9.81 m/s² = 19.62 N

Calculating the Component of Weight Along the Incline

Next, we need to find the component of the weight that acts parallel to the incline. This can be calculated using the sine of the angle of the incline:

• Force parallel to incline (F) = W × sin(θ)

Substituting the values:

• F = 19.62 N × sin(30°) = 19.62 N × 0.5 = 9.81 N

Calculating Work Done

The work done (W_d) in moving the body up the incline can be calculated using the formula:

• Work Done (W_d) = Force (F) × Distance (d) × cos(θ)

In this case, since the force is acting along the direction of the movement (up the incline), we can simplify this to:

• W_d = F × d

Substituting the values we have:

• W_d = 9.81 N × 4 m = 39.24 J

Final Result

Thus, the work done in pulling the body up the inclined plane is 39.24 joules. This calculation illustrates how forces and angles play a crucial role in determining the work done in physical scenarios involving inclined planes.