Forces in Two Dimensions - Mission F2D2 Detailed Help

Consider the physical situation shown below. A 28.5-Newton force is applied at a 30-degree angle to the horizontal to accelerate a 6.5-kg box across a rough surface (coefficient of friction = 0.22). Use g = 9.8 m/s/s to fill in all the blanks and determine the acceleration of the box. Enter each answer accurate to the first decimal place.

(Note: Your numbers are selected at random and likely different from the numbers listed here.)


 
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Success on this question demands an understanding of the mathematical relationships between quantities and an effective strategy. The following strategy will serve you well (if you use it):
  1. Determine the components of the applied force using the equations in the Math Magic section. Write the result down accurate to several decimal places and label each component (Fx= ... , Fy= ...).
  2. Determine the force of gravity (see Formula Frenzy section if needed). Enter the answer into the blank.
  3. Determine the normal force acting upon the object by analyzing the three vertical components. Recognize that the normal force supplies the difference between the downward force of gravity and the vertical component of the applied force. Enter the answer into the blank.
  4. Using the unrounded value for the normal force, determine the force of friction (see Formula Frenzy section if needed). Enter the answer into the blank.
  5. Determine the net force by analyzing the two horizontal forces (Fx and Ffrict). Be sure to use unrounded numbers in your calculation.
  6. Use Newton's second law equation to determine the acceleration of the object. Enter the answer into the blank.

If your answer is incorrect, you will be told which blanks are incorrect and given an opportunity to correct it before the answers are counted as wrong.


 
The applied force has a rightward and an upward component or effect on the box. The rightward component can be calculated as Fapp• cosine(Θ) where Θ is the angle that the force makes with the horizontal. The upward component can be calculated as Fapp• sine(Θ) where Θ is the angle that the force makes with the horizontal.

Fapp-x= Fapp• cosine(Θ)

Fapp-y= Fapp • sine(Θ)


 
The force of friction experienced by an object is often calculated using the equation:        

Ffrict= mu • Fnorm

where mu is the coefficient of friction (dependent predominantly upon the nature of the two surfaces that are in contact) and Fnorm is the normal force.
 
The force of gravity (Fgrav) acting upon an object can be determined from the mass of an object using the equation: 
Fgrav= mass • g

where g is the acceleration caused by gravity. The value of g on Earth is 9.8 m/s/s.