to push a 25 crate up a 27 incline, a worker exerts a force of 120 N, parallel to the incline. As the crate slides 3.6m how much work is done on the crate by a) the worker b) force of gravity c) normal force

To determine the work done on the crate by the worker, the force of gravity, and the normal force, we need to apply the concept of work in physics. Work is defined as the product of the force applied to an object and the distance over which that force is applied, taking into account the angle between the force and the direction of motion.

Calculating Work Done by the Worker

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

Work = Force × Distance × cos(θ)

In this case, the worker exerts a force of 120 N parallel to the incline, and the distance moved by the crate is 3.6 m. Since the force is applied in the same direction as the movement, the angle θ is 0 degrees. The cosine of 0 degrees is 1.

Substituting the values:

Work by Worker = 120 N × 3.6 m × cos(0°) = 120 N × 3.6 m × 1 = 432 J

Calculating Work Done by the Force of Gravity

The force of gravity acts vertically downward, while the crate moves along the incline. To find the work done by gravity, we first need to determine the component of the gravitational force acting along the incline.

The gravitational force can be calculated as:

Weight = mass × gravity

Assuming the mass of the crate is 25 kg and using the acceleration due to gravity as approximately 9.81 m/s²:

Weight = 25 kg × 9.81 m/s² = 245.25 N

Next, we find the component of this weight acting parallel to the incline. The angle of the incline is 27 degrees, so the force of gravity acting down the incline is:

Force of Gravity Along Incline = Weight × sin(27°)

Force of Gravity Along Incline = 245.25 N × sin(27°) ≈ 245.25 N × 0.454 = 111.1 N

Now, we can calculate the work done by gravity:

Work by Gravity = Force of Gravity Along Incline × Distance × cos(180°)

Since the force of gravity acts in the opposite direction to the movement, the angle is 180 degrees, and cos(180°) is -1:

Work by Gravity = 111.1 N × 3.6 m × (-1) = -399.96 J

Assessing Work Done by the Normal Force

The normal force acts perpendicular to the direction of motion. Since work is only done when a force has a component in the direction of movement, the work done by the normal force is zero:

Work by Normal Force = Normal Force × Distance × cos(90°) = Normal Force × 3.6 m × 0 = 0 J

Summary of Work Calculations

• Work done by the worker: 432 J
• Work done by the force of gravity: -399.96 J
• Work done by the normal force: 0 J

In summary, the worker does positive work on the crate, while gravity does negative work, indicating that it opposes the motion. The normal force does not contribute to the work done since it acts perpendicular to the direction of movement. This analysis helps us understand the dynamics of forces acting on objects on an incline.