While sliding a couch across a floor, Andrea and Jennifer exert forces FA and F on the couch. Andrea's force is due north with a magnitude of 140.0 N and Jennifer's force is 260 east of north with a magnitude of 220.0 N (a) Find the net force (in N) in component form. net : (b) Find the magnitude (in N) and direction (in degrees counterclockwise from the east axis) of the net force magnitude direction X o counterclockwise from the east axis (c) If Andrea and Jennifer's housemates, David and Stephanie, disagree with the move and want to prevent its relocation, with what combined force Fos (in N) should they push so that the couch does not move? (Express your answer in vector form.) Fos

See the answers and the explanation below.

Explanation:

To solve this problem we must make a free body diagram with the forces applied as well as the direction. In the attached images we can see the nomenclature of the direction of the forces and the free body diagram.

a)

Sum of forces in y-axis

Fy = 140 - (220*sin(10))

Fy = 101.8 [N]

Sum of forces in x-axis

Fx = - (220*cos(10))

Fx = - 216.65 [N]

b)

For the above result, for there to be balance we realize that we need one equal to the resulting y-axis but in the opposite direction and another opposite force in direction but equal in magnitude on the x-axis.

Fy = - 101.8 [N]

Fx =   216.65 [N]

c )

Now we need to use the Pythagorean theorem to find the result of these forces.

And the direction will be as follows.

α = tan^(-1) (101.8 / 216.65)

α = 25.16° (south to the east)

F = 216.65 i - 101.8 j [N]

note: the given question is incomplete.

complete question is given below.

which is an example of kinetic energy?

a. the energy stored in ethanol  

b. a hockey puck sliding across the ice  

c. a compressed spring  

d. a ball sitting at the top of a ramp

solution: the kinetic energy is the energy posses by the virtue of the motion of the object.

in the given options, a, c and d are the example of potential energy because it is the energy posses by the virtue of the rest of the object. but option b has the kinetic energy as the object is in motion.

hence, a hockey puck sliding across the ice   is the apex example of kinetic energy.

so, the option (b) a hockey puck sliding across the ice   is the correct option.