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A force F

S
1 of magnitude 6.00
units acts on an object at the origin in a direction u 5 30.0° above
the positive x axis (Fig. P3.10). A
second force F
S
2 of magnitude
5.00 units acts on the object in
the direction of the positive
y axis. Find graphically the magnitude and direction of the resultant force F
S
1 1 F
S
2.

User Tayyab
by
7.4k points

2 Answers

5 votes

Answer:

To find the magnitude and direction of the resultant force F1 + F2, we can use the parallelogram method or the tail-to-tail method.

Using the parallelogram method, we would begin by drawing the vectors F1 and F2, with F1 having a magnitude of 6.00 units and a direction of 30.0° above the positive x axis, and F2 having a magnitude of 5.00 units and a direction of the positive y axis. We would then draw a diagonal from the tail of F1 to the head of F2 and another diagonal from the tail of F2 to the head of F1. The point where the diagonals intersect is the head of the resultant vector F1 + F2.

Using the tail-to-tail method, we would begin by placing the tail of F1 at the tail of F2, then drawing a vector from the head of F1 to the head of F2. The resulting vector would be the same as the one obtained with the parallelogram method.

The magnitude of the resultant force F1 + F2 can be found by using the Pythagorean theorem. The horizontal component of the force is 6.00cos(30) = 5.00 units and the vertical component is 6.00sin(30) = 3.00 units. So, the magnitude is sqrt(5^2 + 3^2)= sqrt(25+9) = sqrt(34) = 5.83 units.

The direction of the resultant force F1 + F2 can be found by using trigonometry. The tangent of the angle is 3/5, so the angle is arctan(3/5) = approximately 36.87 degrees counterclockwise from the positive x-axis.

So, the magnitude of the resultant force is 5.83 units and the direction is 36.87 degrees counterclockwise from the positive x-axis.

User Your Friend Ken
by
7.0k points
0 votes

Answer:

To find the magnitude and direction of the resultant force F₁ + F₂, you can use the following graphical method:

Draw an arrow to represent F₁ with a length of 6.00 units and an angle of 30.0° above the x-axis. Then draw an arrow to represent F₂ with a length of 5.00 units and an angle of 90° along the y-axis. Finally, draw a vector connecting the two arrows to represent the resultant force. The magnitude of the resultant vector can be measured with a ruler, and the direction can be measured with a protractor. The magnitude of the resultant vector is approximately 8.06 units, and the direction is approximately 35.9° above the x-axis.

User Brandon Cuff
by
7.5k points