Video: Solving F_net = m•a Problems

We provide the transcript below to those who for whatever reason would find the written words to be preferred over in addition to the actual video. 

Solving F_net = m•a Problems

 
  
Introduction
Most Physics courses will include problems like this one in which you're given force and mass information and must calculate the acceleration. How do you use the Newton's Second Law equation to analyze and solve for acceleration? I'm Mr. H and I have some answers for you.
 
The F_net= m•a Equation
A highly popularized equation in Physics is F_net= m•a. It is often written as a = F_net/m and referred to as Newton's Second Law. It expresses the relationship between acceleration (a), net force (F_net), and mass (m). F_net= m•a is often used to calculate an acceleration or an individual force value ... to solve problems like this one.
 

Important Mathematical Relationships

To solve a Newton's Second Law problem you must understand a variety of math besides F_net= m•a. First you need to know how F_netrelates to individual force values. The net force is the combined effect of all individual forces. It is often determined from a force diagram. The individual forces are represented by vector arrows; their numerical values are listed. The effect of the vertical forces cancel. The right force is bigger than the left by 25 N. The F_net is 25 N, right. Second, the down force is almost always F_grav. It is related to mass by the equation F_grav= m•g where g = 9.8 N/kg. Third, know that vertical forces balance when there is no vertical acceleration. This allows you to equate the up force (often F_norm) to the down force (F_grav). Fourth, sometimes you must calculate the force of friction (F_frict) from the normal force (F_norm) and the coefficient of friction (µ). Use F_frict= µ•F_norm.

 

Two Types of Problems
There are two general types of problems. In the first type, all individual force values are either given or can be calculated from given information. You can use these values to calculated F_net and then acceleration. In the second type, you're given the mass, acceleration, and some force values. You must calculate F_net and then use it to find the unknown value of an individual force. I will do an example of each type.
 

Type 1: Solving for Acceleration
Here is an example of a Type 1 problem. (Pause) Whenever possible, use the given info and your math relationships to calculate as many force values as possible. Record on the diagram. Calculate F_grav. Equate this with F_norm. Calculate F_frict. Now all force values are known. Determine the F_net. Vertical forces balance; they add to 0 N.  Subtract the smaller from the larger horizontal force. Now use Newton's Second Law to calculate acceleration.
 

Type 2: Solving for an Individual Force Values
Here is an example of a Type 2 problem. (Pause) Calculate as many individual force values as you can ... like Fgrav, Fnorm, and Frict. You won't be able to immediately calculate all individual force values - like F_app. The acceleration is given in these types of problems. Use it with mass to calculate the net force (F_net= m•a). Indicate the direction of F_net ... always the same direction as a. Now use F_net to calculate the unknown force - F_app in this problem. If the F_net is directed right, then the right force is bigger than the left force by F_net. You can write F_right = F_left+ F_net. If the left force is bigger than the right force, then you can write F_left= F_right+ F_net. Use one of these two equations to solve for the unknown force value. In this case, F_app is 34 N larger than F_frict.
 

Only Three Forces?
Sometimes students are stumped when there is only one horizontal force. No need to be. The horizontal force - whether it be F_frict, F_app, or F_tens- is the unbalanced force and equal to F_net. The math is actually simpler in these situations.
 

Conclusion
It takes practice to perfect a Physics skill. The Description section of this video has links to some awesome interactive practice exercises on our website. Take a look. Give one a try. Make sure you got this.  Hey I'm Mr. H. Thanks for watching!


 

 

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