Forces in 2D Legacy Problem #3 Guided Solution
Problem*
Helen is parasailing. She sits in a seat harness which is attached by a tow rope to a speedboat. The rope makes an angle of 51° with the horizontal and has a tension of 350 N. Determine the horizontal and vertical components of the tension force.
Audio Guided Solution
Helen is parasailing and as such there are numerous forces acting up on her as she sits in her seat harness. One of the forces is a tension force that is applied downwards at 51 degrees with respect to the horizontal and having a magnitude of 350 Newtons. As with all forces exerted at angles with respect to the horizontal, this force would have a horizontal and a vertical component. These components describe the effect of the force in both the horizontal and the vertical direction and they can be determined if we use trigonometric functions such as sine and cosine. To determine the horizontal and vertical components you should begin by sketching a force arrow. Sketch it in such a way that it makes a 51 degrees angle with the horizontal and label it as 350 Newtons or at least as tension. The 350 Newtons represents the hypotenuse of a right triangle. The right triangle can be constructed if you go to the arrowhead of the vector and draw a vertical line and then go to the tail of the vector and draw a horizontal line. Once you do that you will observe that you have a right triangle and the right angle is at the location where these horizontal and vertical lines intersect. Now you can determine the horizontal side of this right triangle which would be the Fx vector or horizontal component if you use the cosine vector. After all the 51 degrees is the angle between this diagonal force and the horizontal line so the side adjacent to 51 degrees is the horizontal side. To determine its magnitude you would go to the hypotenuse value multiplied by the cosine of 51 degrees. That would be 350 Newtons times the cosine of 51 degrees. To find the vertical side you would need to use the sine function. After all the vertical side is the side opposite the 51 degrees so we can calculate its magnitude if we go 350 Newtons times the sine of 51 degrees. Using sine and cosine functions the horizontal and vertical components can always be calculated through the knowledge of the hypotenuse or the value of the force and the angle that it makes with either the horizontal or the vertical.
Solution
\(F_\text{tension-horizontal} = \units{220}{N}\)
\(F_\text{tension-vertical} = \units{270}{N}\) (rounded from 272 N)
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities in an organized manner. Equate given values to the symbols used to represent the corresponding quantity - e.g., \(m = \units{1.25}{kg}\), \(µ = 0.459\), \(v_o = \units{0.0}{\unitfrac{m}{s}}\), \(θ = 41.6°\), \(v_f = \colorbox{gray}{Unknown}\).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
Read About It!
Get more information on the topic of Forces in 2D at The Physics Classroom Tutorial.