Two forces P and Q whose resultant is 10Newton are at right angles to each other. If P makes 30 degrees with resultant.Show me the workings of the magnitude of Q in Newton and the diagram of the vectors.
To determine the magnitude of force Q and create a diagram of the vectors, we can use vector addition and trigonometry.
Let's assume that force P has a magnitude of P Newton and force Q has a magnitude of Q Newton. Since the resultant of forces P and Q is 10 Newton, we can write the equation:
P^2 + Q^2 = 10^2 = 100
Next, we know that force P makes an angle of 30 degrees with the resultant. Since the resultant is the vector sum of P and Q, we can consider the angle between P and Q as 90 degrees (since they are at right angles to each other) minus 30 degrees (the angle between P and the resultant), which gives us 60 degrees.
Now, to find the magnitude of force Q, we can use the trigonometric relationship:
Q = P * tan(theta)
where theta is the angle between forces P and Q, which is 60 degrees.
Using this equation, we can calculate the magnitude of Q:
Q = P * tan(60 degrees)
To create a diagram of the vectors, we can draw a coordinate system and represent the forces as arrows. The length of each arrow represents the magnitude of the force, and the angle of the arrow represents the direction of the force. In this case, since we have a right angle, we can draw a horizontal and vertical axis and represent force P along the horizontal axis and force Q along the vertical axis.
Unfortunately, as a text-based AI, I cannot provide you with a visual representation of the diagram. However, you can easily create the diagram by drawing a horizontal line for P and a vertical line for Q, both starting from the origin of the coordinate system.
To summarize:
- Use the equation P^2 + Q^2 = 100 to find the magnitude of Q.
- Use the equation Q = P * tan(60 degrees) to determine the magnitude of Q in Newtons.
- Draw a horizontal line for P and a vertical line for Q to create the diagram of the vectors.