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 deg above the the + x-axis, F2 = 2.5 N in the +x-direction, F3 = 3.5 N at 45 deg 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?
(a) Add up the four forces as vectors and see if there is an net x component in the resultant vector. If there is, the motion will deviate from the y axis.
(b) The answer is called the "equilibrant" and is equal to the negative of the resultant vector you got in (a). It has the same magnitude as the resultant but s in the opposite direction.
To determine whether the object will continue to move along the y-axis or not, we need to analyze the net force acting on the object in the y-direction.
(a) To find the net force in the y-direction, we need to resolve each force into its y-component. Let's calculate the y-component of each force:
F1y = F1 * sin(theta1)
= 5.0 N * sin(37 deg)
F2y = F2 * sin(theta2)
= 2.5 N * sin(0 deg) (since the force is in the +x direction)
F3y = F3 * sin(theta3)
= 3.5 N * sin(-45 deg)
F4y = F4
Note: Since F4 is already in the y-direction, we don't need to resolve it further.
Next, we calculate the net force in the y-direction by adding up all the y-components of the forces:
Net Fy = F1y + F2y + F3y + F4y
Now, we substitute the given values and calculate Net Fy:
Net Fy = (5.0 N * sin(37 deg)) + (2.5 N * sin(0 deg)) + (3.5 N * sin(-45 deg)) + 1.5 N
After evaluating this expression, we find the value of Net Fy. If the Net Fy equals zero, then the object will continue to move along the y-axis. If the Net Fy is not zero, then external force is required for the object to continue moving along the y-axis.
(b) If the object does not continue to move along the y-axis, we need to find the simultaneously applied force that will keep it moving at a constant speed.
In this case, we need to determine the magnitude and direction of the external force. The magnitude of the external force should be equal to the magnitude of the Net Fy calculated in part (a).
To determine the direction, we need to sum up all the y-components of the forces acting on the object and the external force. The direction of the external force should be such that it cancels out the resultant y-component force, making the net force zero in the y-direction.
By calculating the magnitudes and directions, you can find the external force required to keep the object moving along the y-axis at a constant speed.