A,1.5kg,object,moves,up,the,y,axis,at,a,constant,speed.When,it,reaches,the,origin,the,force,F1=5.0N,at,37,deg,above,the,+x,axis,F2,=2.5N,in,the,+x,direction,F3=,3,5N,at,45,deg,below,the,neg,x,axis,and,F4,=,1.5N,in,the,neg,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?
If all the components of all forces in the x direction are zero, it will not accelerate right or left.
If they do not add to zero, it will move right or left.
If you want it to be zero, and it is not, add a force with an equal and opposite x component.
To determine whether the object will continue to move along the y-axis, we need to find the net force acting along the y-axis.
(a) The forces acting along the y-axis are F4 = -1.5N and F1sin(37) = 5.0N * sin(37). Since F4 is in the negative y-direction, it is opposing the motion along the y-axis. To find the net force, we subtract the force in the negative direction from the force in the positive direction:
Net force in the y-direction = F1sin(37) - F4
= 5.0N * sin(37) - (-1.5N)
= 3.03N - (-1.5N)
= 4.53N
Since there is a net force of 4.53N acting in the positive y-direction, the object will continue to move along the y-axis.
(b) If the object were not moving along the y-axis at a constant speed, there must be a net external force acting on it in the y-direction. To keep it moving along the y-axis at a constant speed, the magnitude of the net external force in the y-direction should be equal to the opposing net force of 4.53N.
Therefore, a force with a magnitude of 4.53N should be applied in the negative y-direction to balance the forces and keep the object moving along the y-axis at a constant speed.
To determine if the object will continue to move along the y-axis, we need to analyze the forces acting on it.
First, let's resolve the forces in the x and y directions:
- F1 is at 37 degrees above the +x axis, so its vertical component is F1_y = F1 * sin(37°)
- F2 is in the +x direction, so it has no vertical component (F2_y = 0)
- F3 is at 45 degrees below the -x axis, so its vertical component is F3_y = F3 * sin(45°)
- F4 is in the -y direction, so its vertical component is F4_y = -F4
Now, let's sum the vertical components of the forces:
Sum of vertical forces (ΣF_y) = F1_y + F2_y + F3_y + F4_y
If the sum of the vertical forces is zero (ΣF_y = 0), then the object will continue to move along the y-axis at a constant speed. However, if the sum of the vertical forces is not zero, there will be a net force acting perpendicular to the y-axis, causing the object to deviate from its original path.
Assuming the angles provided in the problem are measured from the positive x-axis, we can plug in the values:
ΣF_y = F1 * sin(37°) + 0 + F3 * sin(45°) + (-F4)
Now, we can calculate the value of ΣF_y and answer the questions:
(a) If ΣF_y = 0, then the object will continue to move along the y-axis. If ΣF_y ≠ 0, then the object will not continue to move along the y-axis.
(b) If the object does not continue to move along the y-axis, we need to find the force that will keep it moving along that axis at a constant speed. In this case, we need to apply a force with a vertical component equal in magnitude but opposite in direction to ΣF_y.