Three forces of magnitudes , , and are applied to a block of mass , initially at
ID: 2007386 • Letter: T
Question
Three forces of magnitudes , , and are applied to a block of mass , initially at rest, at angles shown on the diagram. 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).A. Calculate the magnitude of the resultant force acting on the block.
Express the magnitude of the resultant force in newtons to two significant figures.
B. What angle does make with the positive x axis?
What is the magnitude of the block's acceleration vector, ?
Express your answer to two significant figures.
C.What is the magnitude of the block's acceleration vector, ?
Express your answer to two significant figures.
D.What is the direction of ? In other words, what angle does this vector make with respect to the positive x axis?
E.How far (in meters) will the block move in 5.0 ? Recall that it starts from rest.
Explanation / Answer
if you already have the magnitude of the three forces, break them down into components and add the components respectively. The result will be the components of the resultant vector which you can use to find the angle it makes with the positive axis using the definition of tangent (may need to adjust the angle to the first quadrant). Use Pythagorean theorem to find the magnitude of that resultant force, and divide it by the mass to find the acceleration. It's direction is the same as the resultant force's. Finally, use the equation x=vit + (1/2)at^2 with vi=0 and t=5 to find the displacement.