1. I don't understand!

A 1.5-kg object moves up the y-axis at a constant speed. When it reaches the origin, the forces F1 = 5.0 N at 37o above the +x-axis, F2 = 2.5 N in the +x-direction, F3 = 3.5 N at 45o below the -x-axis, and F4 = 1.5 N in the -y-direction are applied to it. (a) Will the object continue to move along the y-axis? (b) If not, what simultaneously applied force will keep it moving along the y-axis at a constant speed?

2. Well, add up all the forces (using vector addition) to find out what the net force is acting on the object, call it $\Sigma F$.

i.e. $\Sigma F = F_1 + F_2 + F_3 + F_4$.

For part (a), if the angle of $\Sigma F$ is along the y-axis, or if its magnitude is zero, then the object will stay on the y-axis.

For part (b), apply a force of the same magnitude but opposite direction (that is, apply $-\Sigma F$) to allow the object to continue along the y-axis at its original speed.

3. Originally Posted by Celia
A 1.5-kg object moves up the y-axis at a constant speed. When it reaches the origin, the forces F1 = 5.0 N at 37o above the +x-axis, F2 = 2.5 N in the +x-direction, F3 = 3.5 N at 45o below the -x-axis, and F4 = 1.5 N in the -y-direction are applied to it. (a) Will the object continue to move along the y-axis? (b) If not, what simultaneously applied force will keep it moving along the y-axis at a constant speed?
Hello,

I've attached a diagram to clarify(?) the situation described by your problem.

to a) The blue vectors are

$\overrightarrow{\overrightarrow{F_1}+ \overrightarrow{F_2} }\ \mbox{and}\ \overrightarrow{\overrightarrow{F_3}+ \overrightarrow{F_4} }$

then I added these vectors and got the result (=red vector). It has a value of 4.133 N and forms an angle of -13.5° with the x-axis.

to b) the object will move on undisturbed if all applied forces have the value 0. So applie a force $\overrightarrow{F_5}$ which has the value of the red resulting vector and points in the opposite direction.

Greetings

EB