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.
P = 10*Cos30 = 8.66 N.
Q = 10*Cos(90-30) = 5 N.
50N
Two forces Aand B whose resultant is 12Newton are at right angles triangle to each other. If P makes 90 degrees with resultant.Show me the workings of the magnitude of Q in Newton and the diagram of the vectors.
Well, I have to say, this is going to be a bit of a balancing act! But don't worry, I'll try my best to make it funny and easy to understand.
First, let's break down the problem step by step. We have forces P and Q, with a resultant of 10 Newton. They are at right angles to each other. This is starting to sound like a bad joke, isn't it? Two forces walk into a bar... I mean, act on an object!
Now, P makes an angle of 30 degrees with the resultant. Okay, let's visualize this. Imagine a right-angled triangle, where the resultant is the hypotenuse and P is one of the sides. Since the angle between P and the resultant is 30 degrees, we have a bit of a trigonometry challenge here.
To find the magnitude of Q, we can use some trigonometric magic. The formula we need is Q = R * sin(theta), where R is the magnitude of the resultant and theta is the angle between Q and the resultant. In our case, theta is 90 degrees. However, since sin(90) is 1, we don't need to worry about Q being a zero! Phew!
Now let's put all this math into action and draw a diagram. But be warned, my artistic skills might be a bit... let's just say, questionable.
|
|
R |
|_____P (30 degrees)
|
|
│
Q │
Please excuse my crude drawing, I'm more of a stand-up comedian than an artist. But I hope you get the idea!
So, to sum it all up, the magnitude of force Q can be found using the formula Q = R * sin(theta), where R is 10 Newton and theta is 90 degrees. Plug in those values, and you'll have the answer! And don't forget to laugh a little along the way. After all, a little humor makes everything easier to remember.
To find the magnitude of force Q in Newton, we can use basic trigonometry. Let's break down the problem step by step.
Step 1: Draw a diagram illustrating the given information.
P
|
|
|\
| \
| \ Q
| \
------|----\
| \
| \
| \
Resultant \
\
\
\
\
Here P and Q represent the forces, and the angle between P and the resultant is given as 30 degrees. The resultant force is represented by a straight line.
Step 2: We know that the resultant force is the sum of force P and force Q.
So, we can use the Pythagorean theorem to find the magnitude of force Q. According to the theorem, the square of the hypotenuse (resultant) is equal to the sum of the squares of the other two sides (P and Q):
resultant^2 = P^2 + Q^2
Step 3: Substitute the given values into the equation.
resultant^2 = 10 N^2 (given)
P = 10 N (given)
resultant^2 = (10 N)^2 + Q^2
resultant^2 = 100 N^2 + Q^2
Step 4: Solve for Q^2 by isolating the term on one side of the equation.
Q^2 = resultant^2 - 100 N^2
Step 5: Calculate the magnitude of Q by taking the square root of Q^2.
Q = √(resultant^2 - 100 N^2)
Substituting the given values:
Q = √(10 N^2 - 100 N^2)
Q = √(-90 N^2) (Note: the square root of a negative number is not defined in the real number system, so we have an imaginary result)
Therefore, in this case, the magnitude of Q is not defined in Newton because it leads to an imaginary result.