At a picnic, there is a contest in which hoses are used to shoot water at a beach ball from three directions. As a result, three forces act on the ball, F1, F2, and F3 (see drawing). The magitudes of 1 and 2 are F1 = 55.0 newtons and F2 = 95.0 newtons. Using a scale drawing and the graphical technique determine the following such that the resultant force acting on the ball is zero.
i'm not sure how to start this problem
help pleasee
the answer above is for another calculation so plug in you values and derive your answer
To solve this problem, you can use the graphical technique called the polygon method. Here are the steps to follow:
1. Draw a scale diagram representing the magnitudes and directions of the three forces acting on the beach ball. Start by drawing a reference line to represent one of the forces. Let's choose F1 and draw it to scale, making sure to indicate its direction. Label it F1 = 55.0 N.
2. From the endpoint of F1, draw a line representing the second force, F2 = 95.0 N, using the same scale as in Step 1. Again, indicate the direction.
3. From the endpoint of the resultant of F1 and F2, draw a line representing the third force, F3. This line should be drawn with the same scale as in Steps 1 and 2. Make sure to indicate the direction of F3.
4. Connect the starting point of F1 to the endpoint of F3 to complete the polygon.
5. Measure the length and direction of the line connecting the starting point of F1 to the endpoint of F3 to determine the magnitude and direction of the resultant force.
6. If the length of the line from Step 5 is equal to zero (or very close to zero), then the resultant force acting on the ball is zero. Otherwise, adjust the scale or the accuracy of your measurement and repeat Steps 2-5 until the resultant force equals zero.
By following these steps, you should be able to determine the forces F3 and its direction needed in order to have a resultant force equal to zero.
To solve this problem, we can use the graphical technique called vector addition or the triangle method. Here's how you can approach it step by step:
Step 1: Draw a scale diagram representing the forces F1 and F2 acting on the beach ball. Use a ruler to make sure your drawing is accurate.
Step 2: Choose a suitable scale for your diagram that allows you to work with manageable numbers. For example, you could choose a scale of 1 cm = 10 N.
Step 3: Draw a vector representing F1 with an arrow showing its direction. The length of this vector should be proportional to the magnitude of F1. In this case, F1 = 55 N, so you could draw a vector 5.5 cm long.
Step 4: Draw a vector representing F2 with an arrow showing its direction. Again, the length of this vector should be proportional to the magnitude of F2. In this case, F2 = 95 N, so you could draw a vector 9.5 cm long. The direction of F2 should be different from that of F1; choose an angle that seems logical based on the description of the problem.
Step 5: Use a ruler to measure the length of the resultant vector that you formed by connecting the tail of F1 to the head of F2. The magnitude of this resultant vector should be zero because the problem asks for the resultant force acting on the ball to be zero.
Step 6: Now, use the scale you chose (1 cm = 10 N) and measure the length of the resultant vector. It should be zero. If it's not, adjust the angle and length of F2 until the resultant vector is zero.
Step 7: Finally, measure the angle between the resultant vector and the initial direction of F1 (or any other reference direction). This will give you the direction of F3, the third force that needs to be applied to the ball to make the resultant force zero.
Remember, the scale diagram is just a visual aid to help you solve the problem. The measurements on the diagram aren't the actual values of the forces, but they allow you to determine the required magnitude and direction.
Figure out the East-West forces and add them up:
... from F1: 40 cos(60 deg) = 20
... from F2: -90
... from F3: F3 cos(theta)
Add them up:
... -70 + F3 cos(theta)
Set it equal to zero (the ball does not move)
... 70 = F3 cos(theta)
Now do the same for the North-South forces. You should get
... 34.641 = F3 sin(theta)
We have two equations in two unknowns. We can solve them, first for the angle:
34.641 / 70 = [-F3 sin(theta) ] / [F3 cos(theta) ]
0.4949 = -tan(theta)
Using arctangent, we find
theta = 26.33 degrees.
And cos(theta) = 0.896
and sin(theta) = 0.444
Putting these back into the first two equations:
70 = F3 cos(theta)
70 / 0.896 = F3 = 78.102
And also
34.641 = F3 sin(theta)
34.641 / 0.444 = F3 = 78.102