Forces in 2D Legacy Problem #1 Guided Solution
Problem*
For each collection of listed forces, determine the vector sum or the net force.
Set A
- 58 N, right
- 42 N, left
- 98 N, up
- 98 N, down
Set B
- 14 N, left
- 16 N, up
- 16 N, down
Set C
- 12 N, up
- 8 N, down
Audio Guided Solution
The net force acting upon an object is defined as the vector sum of all the individual forces which act upon it. So if you know the magnitude and the direction of all the individual forces, you should always be able to determine the net force. When we speak of the vector sum in physics, what we mean is you're adding, summing, two forces and you're considering both their magnitude and their direction. Now when we look at set A, we observe that there are four individual forces acting upon the object and of the four, two of them have equal magnitude. One is 98 newtons up and the other is 98 newtons down. When you add these two forces up, you get zero newtons. In other words, we would say they balance each other. There are two remaining forces in set A that have yet to be added. One is 58 newtons to the right and the other is 42 newtons to the left. If you consider that 42 newtons to the left to be the same as negative 42 newtons, you could add it to the 58 newtons to the right when treated as a positive 58. When doing so, you'll observe that there is positive 16 newtons left, where we have defined positive as to the right. So the net force in set A is 16 newtons to the right. In set B, we observe there are three forces acting upon the object and two of them are equal in magnitude and opposite in direction. When you add the 16 newtons up to the 16 newtons down, they add up to zero newtons. What you have remaining is 14 newtons to the left. So the net force, or vector sum of all the forces, in set B is 14 newtons to the left. In set C, there is no actual balancing of any of the up, down, or left, right forces, but there is some partial cancellation of the 12 newtons up by the 8 newtons down. When you go 12 newtons up plus 8 newtons down, what you have remaining is 4 newtons, and that's up. You get to that 4 newtons up by treating 8 newtons down as being negative 8 newtons and adding it to the positive 12 newtons up. Here, I am defining up to be the positive direction, so it's at positive 12 newtons plus negative 8 newtons adds up to positive 4 newtons. Again, positive has been defined as the upward direction. So that's 4 newtons up as a net force.
Solution
Set A: \(\sum{F}^{} = \units{16}{N}\), right
Set B: \(\sum{F}^{} = \units{14}{N}\), left
Set C: \(\sum{F}^{} = \units{4}{N}\), up
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.