how do you do newtons vector 2nd law and newtons third law of motion?

Question

i have a homework problem i have been workin on for hours now and i cant understnad it .....
A ducks mass = 2.9 kg. As the duck paddles, a force of 0.08 N acts on it in a direction due east. the current of the water exerts a force of 0.27 N in a direction of 41° south of east. When these forces begin to act, the velocity of the duck is 0.12 m/s due east. what is magnitude and the direction (relative to due east) of the displacement ofthe duck after 3.4 s while the forces are acting.

that is my homework problem i would like someone not to do it for me but maybe talk me through how to set up a problem like this so i can learn it myself...

Answer 1

You can try to draw vector diagram and use displacement equations and also cosine rule to solve it.

Answer 2

When dealing with any force-motion problem, the FIRST thing you must do is ID ALL THE FORCEs acting on the body (mass).

Then, ADD UP all the forces acting on the mass (duck) in the X direction and then in the Y direction (assuming Cartesian coordinates). You will end up with two net force equations: one for X and one for Y.

Finally invoke f = ma in some form to solve the two equations. f = net force acting on the body = its mass times its acceleration. So, fx = sum(all forces in X direction) and fy = sum(all forces in Y direction). Remember, these are vectors; so their directions count.

EXAMPLE: your problem

1. ID ALL THE FORCES---F(paddling) = .08 N going east (X direction only); F(current) = .27 N going south east (X and Y components)

2. SUM in X and Y---fx = F(paddling) + F(current) cos(theta); where theta = 41 deg. The two forces are additive because they are both going east. fy = F(current) sin(theta). The current force is the only sideways force, presuming the duck keeps heading east with its paddling force.

3. fx = ma(x) = F(paddling) + F(current) cos(theta)
fy = ma(y) = F(current) sin(theta)

Solve for a(x) and a(y), the accelerations in the x and y directions. Then invoke the SUVAT equation s = ut + 1/2 at^2 to find out how far the duck went after t = 3.4 sec; where u(x) = .12 m/sec velocity east when t = 0 and u(y) = 0 at the start.

Note, you will have two SUVAT equations to solve: one for the X direction and one for the Y. Thus, you will have s(x) and s(y), which are the distances the paddling and current take the duck from t = 0. These two distances form the two sides of a right triangle; thus, S = sqrt(s(x)^2 + s(y)^2) is the hypoteneuse. You can find the angle (omega) with respect to east (X) by s(x) = S cos(omega); so that ARC cos = omega.

There you have it: ID the forces, SUM the forces, and solve the equations using f = ma and SUVAT.

Answer 3

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