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 37 degrees. above the +xaxis, F2 N in the +X direction, F3 = 3.5 N at 45 degrees below the -X axis, and the F4 = 1.5 N in the - y direction are applied to it. a)Will the object continue moving along the y axis? b) if not, what simutaneous applied force will keep it moving along the y axis at a constant speed?
I described how to do this yesterday. Start by adding the four force vectors. Someone will gladly critique your work.
The mass of the object is not needed to answer the questions.
If you are unfamiliar with how to add vectors, please say so and references can be provided.
For my previously posted answer to this question, see
http://www.jiskha.com/display.cgi?id=1200610304
To determine if the object will continue moving along the y-axis, we need to calculate the net force acting on the object in the y-direction.
First, let's resolve the forces into their components:
F1x = F1 * cos(37°)
F1y = F1 * sin(37°)
F2x = F2 (since it acts in the +X direction)
F2y = 0 (since it does not have a component in the y-direction)
F3x = F3 * cos(-45°)
F3y = F3 * sin(-45°)
F4x = 0 (since it does not have a component in the x-direction)
F4y = -F4 (-1.5 N since it is in the -y direction)
Now, let's sum up all the forces in the y-direction:
Net force in y-direction (Fnet_y) = F1y + F2y + F3y + F4y
Fnet_y = F1 * sin(37°) + F3 * sin(-45°) - 1.5 N
a) If the net force in the y-direction is non-zero, it means there is a resultant force acting on the object. Therefore, the object will not continue moving along the y-axis.
b) To keep the object moving along the y-axis at a constant speed, we need to make the net force in the y-direction zero. In this case, we need to find an additional force in the +y direction to balance the forces acting in the -y direction.
Fnet_y = 0
F1 * sin(37°) + F3 * sin(-45°) - 1.5 N = 0
Solving for the additional force:
Additional force in the +y direction = 1.5 N - F1 * sin(37°) - F3 * sin(-45°)
To determine whether the object will continue moving along the y-axis or not, we need to find the net force acting on the object in the y-direction.
a) To find the net force in the y-direction, we need to break down the forces into their y-components and add them up. In this case, the forces acting along the y-axis are F3 and F4.
F3 has a magnitude of 3.5 N and is directed at 45 degrees below the -X axis. To find its y-component, we multiply its magnitude by the sine of 45 degrees (since sine is the ratio of the opposite side to the hypotenuse in a right triangle). So, F3y = 3.5 N * sin(45) = 3.5 N * √2 / 2 = 2.47 N.
F4 has a magnitude of 1.5 N and is directed in the -y direction. Therefore, its y-component is simply -1.5 N.
Now, we can find the net force in the y-direction by adding up the y-components of F3 and F4:
Net Force (F_net_y) = F3y + F4 = 2.47 N + (-1.5 N) = 0.97 N.
Since the net force in the y-direction is non-zero (0.97 N), the object will not continue moving along the y-axis.
b) To keep the object moving along the y-axis at a constant speed when it reaches the origin, we need to apply a force in the y-direction that cancels out the net force acting on the object in the y-direction. In this case, the net force is 0.97 N in the +y direction.
Therefore, to counteract this net force, we would need to apply an opposite force of 0.97 N in the -y direction.
So, to keep the object moving along the y-axis at a constant speed, we need to simultaneously apply a force of 0.97 N in the -y direction.