Problem: The diagram below shows a block of mass m = 2.00 kg on a frictionless horizontal surface, as seen from above. Three forces of magnitudes F4.00 N, F2 6.00 N, and F3 8.00 N are applied to the block, initially at rest on the surface, at angles shown on the diagram. (Figure 1) In this problem, you will determine the resultant (total) force vector from the combination of the three individual force vectors. All angles should be measured counterclockwise from the positive x axis (i.e., all angles are positive). 

FREE Expert Solution

A force can be expressed as:

F=|F|cosθi^+|F|sinθj^

Magnitude:

|F|=Fx2+Fy2

For the three forces, we have:

F1=(4.00)cos (25°)i^+(4.00)sin (25°)j^=(3.62N)i^+(1.69N)j^F2=(6.00)cos (325°)i^+(6.00)sin (325°)j^=(4.91N)i^-(3.44N)j^F3=-(4.00N)i^

View Complete Written Solution
Problem Details

The diagram below shows a block of mass m = 2.00 kg on a frictionless horizontal surface, as seen from above. Three forces of magnitudes F4.00 N, F2 6.00 N, and F3 8.00 N are applied to the block, initially at rest on the surface, at angles shown on the diagram. (Figure 1) In this problem, you will determine the resultant (total) force vector from the combination of the three individual force vectors. All angles should be measured counterclockwise from the positive x axis (i.e., all angles are positive). 

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Vectors with More Trigonometry concept. You can view video lessons to learn Vectors with More Trigonometry. Or if you need more Vectors with More Trigonometry practice, you can also practice Vectors with More Trigonometry practice problems.