A constant force of 900 N pushes a 100 kg mass up the inclined plane shown above at a uniform speed of 5 m/s. ( hight= 1m) The power developed by the 900 N force is most nearly:
400 W
800 W
900 W
1000 W
4500 W
To find the power developed by the 900 N force, we can use the formula:
Power = Force x Velocity
First, let's calculate the velocity component of the object parallel to the inclined plane. To do that, we'll use trigonometry. The angle of the inclined plane can be determined using the vertical distance (height) and the horizontal distance along the inclined plane. In this case, the height is given as 1m, and since the object is moving at a uniform speed of 5 m/s, the horizontal distance (d) covered in one second is also 5m. Therefore, we can determine the angle (θ) using the tangent function:
tan(θ) = height / distance
tan(θ) = 1 / 5
Taking the inverse tangent of both sides:
θ = tan^(-1)(1/5)
Using a calculator, we find that θ is approximately 11.31 degrees.
Next, we need to resolve the force into its components along and perpendicular to the inclined plane.
The perpendicular component of the force can be determined using the equation:
Force_perpendicular = Force x cos(θ)
Force_perpendicular = 900 N x cos(11.31 degrees)
Calculating this, we find that the perpendicular component is approximately 884.54 N.
Since the object is moving at a uniform speed, we know that the net force parallel to the inclined plane is zero. This means that the force parallel to the inclined plane is equal in magnitude but opposite in direction to the force of friction. Therefore, the magnitude of the force parallel to the inclined plane is:
Force_parallel = Force of Friction = 884.54 N
Finally, we can calculate the power developed by the force using the formula:
Power = Force x Velocity
Since the force parallel to the inclined plane is equal in magnitude to the applied force, the power developed by the 900 N force is:
Power = Force_parallel x Velocity
Power = 884.54 N x 5 m/s
Multiplying these values together, we find that the power developed by the 900 N force is approximately 4422.7 W, which is closest to 4500 W from the given options.