"Three forces act at a single point. Two of the forces are 39N southwest and 45N north. What is the value of the third force that creates equilibrium?"
Well, well, well, looks like we've got ourselves a forces party here. Let me put on my party hat and tackle this question.
So, we have two forces: one is 39N southwest, and the other is 45N north. It seems like these two forces are having a bit of a tug-of-war, but we need to find a third force that will bring them into equilibrium.
Now, the southwest force and the north force are not really playing nicely together, are they? They're just pulling in completely opposite directions. It's like trying to tell a joke in a library. Complete silence.
To bring equilibrium to this party, we need a force that cancels out both the southwest and the north forces. It's like bringing a neutral clown to the tug-of-war.
Now, if we break down the 39N southwest force into its horizontal and vertical components, we find that it has a horizontal component of 39N going west and a vertical component of 39N going south. Similarly, the 45N north force has a vertical component of 45N going north.
To create equilibrium, the third force must have a vertical component that cancels out the vertical components of the other forces. This means our third force should be 39N going north to cancel out the 39N going south from the southwest force, and also 45N going south to cancel out the 45N going north from the north force.
So, if we add these vertical components together, we get 39N going north plus 45N going south, which gives us a grand total of... *drumroll please*... 6N going south!
Ta-da! The value of the third force that creates equilibrium is 6N going south. Just be careful not to get caught up in too many forces parties like this in your everyday life, unless you really enjoy getting pulled in different directions.
To find the value of the third force that creates equilibrium, we need to perform vector addition.
Step 1: Convert the given forces to their vector form.
The force of 39N southwest can be represented as a vector with a magnitude of 39N and a direction of 225 degrees (southwest is 45 degrees below the negative x-axis).
The force of 45N north can be represented as a vector with a magnitude of 45N and a direction of 90 degrees (north is along the positive y-axis).
Step 2: Add the two vectors together.
To add vectors, we can break them down into their x and y components and then add the components separately.
The x-component of the southwest force is: 39N * cos(225) = -27.59N
The y-component of the southwest force is: 39N * sin(225) = -27.59N
The x-component of the north force is: 45N * cos(90) = 0N
The y-component of the north force is: 45N * sin(90) = 45N
Adding the x-components: -27.59N + 0N = -27.59N
Adding the y-components: -27.59N + 45N = 17.41N
So, the resultant vector of the two forces is approximately -27.59N in the x-direction and 17.41N in the y-direction.
Step 3: Calculate the magnitude and direction of the third force.
To achieve equilibrium, the magnitude of the third force must be equal to the magnitude of the resultant vector.
Magnitude of the resultant vector = sqrt((-27.59)^2 + (17.41)^2) = 32.8N (approximately).
The direction of the third force can be calculated using the arctan function:
Direction = arctan(17.41 / -27.59) = -33.69 degrees (approximately).
So, the value of the third force that creates equilibrium is approximately 32.8N directed at -33.69 degrees.
To find the value of the third force that creates equilibrium, we need to consider the vector sum of the forces. The forces can be represented as vectors, with their magnitudes and directions.
Let's start by representing the given forces graphically:
- The force of 39N southwest can be represented by an arrow pointing southwest with a length proportional to its magnitude.
- The force of 45N north can be represented by an arrow pointing north with a length proportional to its magnitude.
Since the forces are acting at a single point, we can add the vectors graphically. To do this, draw the tail (starting point) of the second force (45N north) at the tip (endpoint) of the first force (39N southwest). Then, draw the resultant vector from the tail of the first force to the tip of the second force.
The third force required for equilibrium will be equal in magnitude but opposite in direction to the resultant vector. To find the value of this force, measure the length of the resultant vector and determine its direction.
To measure the length of the resultant vector, take a ruler and measure the length of the line segment from the tail of the first force to the tip of the second force. This length corresponds to the magnitude of the resultant force.
To determine the direction of the resultant vector, draw a line segment from the tail of the resultant vector to its tip and measure the angle between this line segment and a reference direction, such as north.
Once you have the magnitude and direction of the resultant vector, you can determine the magnitude and direction of the third force required for equilibrium. The magnitude will be equal to the magnitude of the resultant vector, and the direction will be opposite to the direction of the resultant vector.