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Three forces of magnitudes F_{1}=4.0N, F_{2}=6.0N, and F_{3}=8.0N are applied to a block of mass m=2.0kg, initially at rest, at angles shown on the diagram. (Figure 1) In this problem, you will determine the resultant (net) force by combining the three individual force vectors. All angles should be measured counterclockwise from the positive x axis (i.e., all angles are positive).

**Part A**: Calculate the magnitude of the resultant force F? r=F? 1+F? 2+F? 3 acting on the block.

Express the magnitude of the resultant force in newtons to two significant figures.

**Part B**: What angle does F? r make with the positive x axis?

Express your answer in degrees to two significant figures.

**Part C**: What is the magnitude of the block’s acceleration vector, a?

**Part D**: What is the direction of a? ? In other words, what angle does this vector make with respect to the positive x axis?

Express your answer in degrees to two significant figures.

**Part E**: How far (in meters) will the block move in 5.0 s? Recall that it starts from rest.

Express the distance d in meters to two significant figures.

Concepts and ReasonsThis problem can be solved using the following concepts: component of vector in horizontal or vertical direction, addition horizontal and vertical components separately, Newton’s 2nd law of motion and kinematic equation.

You can calculate the magnitude and angle of the force by using the vertical and horizontal components of the force.

Newton’s Second Law can be described as the sum of the acceleration and the force. You can calculate the acceleration using the Second Law of Newton.

Fundamentals