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Question

1. Draw a force F. Write down the components of the force F in terms of the angle that F makes with a horizontal line and the magnitude.

2. Write down the angle θ in terms of F_x and F_y.

3. Rotate the drawing.

4. Take a frame of reference where x is the horizontal and y is vertical. Draw a force F₁ which has magnitude F = 6N and makes an angle θ = 270 degrees with the horizontal. Calculate the component of the force along x and y.

5. On the same picture, draw a new axis x' that makes an angle of 60 degrees with the old axis x. Draw a y'axis perpendicular to x'. Compute the components of F₁ with respect to x' and y'.

6. Find the component of F₁ parallel to the straight line (call it L) passing through the origin and that makes an angle of 45 degrees with x.

7. Suppose a mass m = 4 kg is subject to F₁. What is the acceleration of the mass along the line L? What is the acceleration of the mass along x?