Question

A person pulls on a 50 kg desk with a 200n force acting at 30° angle above the horizontal. The desk does not budge. Draw a diagram showing the forces that act "on" the desik. Write the equation for the sum of x-components of the forces that act on the desk.

a. Write the equation for the sum of y-components of the forces that act on the desk.
b. Determine the x and y components of the applied force. the value of the frictional force acting on the desk. Do the same for the normal force acting on the desk.

Answer 1

The forces acting on a 50 kg desk with a 200 N force applied at a 30° angle can be analyzed by calculating the x and y components of the applied force, frictional force, and normal force, considering the desk does not move.

Step-by-step explanation:

Determining Forces Acting on a Desk

To analyze the forces acting on the desk, we can draw a free-body diagram and write the equations for the sum of the forces in the x (horizontal) and y (vertical) components.

X-Component Forces

The x-component of the applied force can be calculated using trigonometry: Fx = F * cos(θ), where F is the applied force and θ is the angle above the horizontal.
In this case, Fx = 200 N * cos(30°). The x-component of the frictional force counteracts this force and since the desk does not move, the frictional force is equal in magnitude and opposite in direction to the x-component of the applied force.

Y-Component Forces

The y-component of the applied force is Fy = F * sin(θ), and the desk's weight provides the force of gravity downward, which is 50 kg * 9.8 m/s². The normal force counteracts both the force of gravity and the y-component of the applied force. Since the desk does not move vertically, the sum of the y-components must equal zero,
meaning the normal force is equal to the force of gravity plus the y-component of the applied force.

By calculating these components, we find the x and y components of friction and the normal force applied on the desk.