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Home Minds On Newton's Laws Mission NL9 Force Analysis Help Help 5

Mission NL9 Force Analysis

The Question

Chuck Wagon applies a 300-N force to accelerate a 30-kg box at 2.5 m/s/s. Fill in all blanks in the diagram below and determine the force of friction (in Newtons) encountered by the box. (Use the approximation that g ~ 10 N/kg.) ...
 
(Note: Numbers are randomized numbers and likely different from the numbers listed here.)

Game Plan

The big idea in this problem is to use the acceleration of the object to determine the net force; and then to use the net force to determine the value of an individual force - Ffrict. The following method will assist your solution to the problem.
 
  • The mass and acceleration of the object are explicitly stated. The net force can be determined using Newton's second law equation: Fnet= m • a.
  • One of the four individual forces (Fapp) is explicitly stated. The force of gravity can be determined from the object's mass (see Formula Fix section below; use g = 10 N/kg). Since there is no vertical acceleration, the two vertical forces must balance; thus, the normal force is equal to the force of gravity. Now three of the four individual force values have been determined; all that is left to be determined is the Ffrict value.
  • The net force is the vector sum of all the forces. It has a value (which is the m•a product) and a direction (which is the same direction as the acceleration). The net force tells who wins the tug-of-war between individual forces (that's the direction) and the winning margin in the tug-of-war (that's the value). So if the net force is 30 N, right then the rightward force wins the tug-of-war over the leftward force; and the winning margin is 30 N. That is, the rightward force is bigger than the leftward force by 30 N. Once you have determined the net force by multiplying m•a, determine the friction force by using this principle. Take your time and think about it!

Formula Fix

The mass of an object is mathematically related to its weight by the equation:
 
Weight = Fgrav = mass • g

where g is the gravitational field strength. The value of g on Earth is 9.8 N/kg (approximately 10 N/kg).

 

The relationship between net force (Fnet), mass (m) and acceleration (a) is expressed by the equation:
 
a = Fnet / m

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