Five hockey pucks are sliding across frictionless ice. The drawing shows a top view of the pucks and the three forces that act on each one. The forces can have different magnitudes (F, 2F, or 3F), and can be applied at different points on the puck. Only one of the five pucks could be in equilibrium. Which one?

the puck with the center negative force of 2F and two outer forces on the top and bottom of the puck with +1F.

To determine which puck is in equilibrium, we need to understand the conditions for equilibrium. For an object to be in equilibrium, the net force acting on it must be zero, and the net torque (or moment) acting on it must also be zero.

Let's analyze each puck and evaluate the net force and net torque acting on it:

1. Puck 1: The forces acting on Puck 1 are F, 2F, and 3F. Since the magnitudes of the forces are different, the net force will not be zero. Additionally, if the forces are applied at different points on the puck, it is likely that the torques involved will not cancel each other out. Therefore, Puck 1 is not in equilibrium.

2. Puck 2: Similar to Puck 1, Puck 2 has different magnitudes of forces acting on it (F, 2F, 3F), indicating that the net force will not be zero. Additionally, if the forces are applied at different points on the puck, the torques involved will not likely cancel each other out. Therefore, Puck 2 is not in equilibrium.

3. Puck 3: Again, Puck 3 has different magnitudes of forces acting on it (F, 2F, 3F), indicating that the net force will not be zero. Moreover, if the forces are applied at different points on the puck, the torques involved will not likely cancel each other out. Therefore, Puck 3 is not in equilibrium.

4. Puck 4: The forces acting on Puck 4 are 2F, F, and F. While the magnitudes of forces differ, we can rearrange the forces such that a pair cancels each other out. Here, we can assume that the forces with magnitudes F and F are located on opposite sides of the puck. This way, the torques caused by those forces will cancel each other out, resulting in a net torque of zero. Additionally, since the magnitudes of these two forces are equal, the net force will also be zero. Therefore, Puck 4 is in equilibrium.

5. Puck 5: Puck 5 also has forces with magnitudes 2F, F, and F. Similar to Puck 4, if we arrange these forces in a way that the two forces with magnitude F are on opposite sides of the puck, their torques will cancel each other out, resulting in a net torque of zero. However, the net force will not be zero since the magnitudes of the forces are different. Therefore, Puck 5 is not in equilibrium.

In conclusion, only Puck 4 is in equilibrium.

To determine which puck could be in equilibrium, we need to consider the forces acting on each puck.

In order for an object to be in equilibrium, the net force acting on it must be zero. This means that the sum of all the forces acting on the puck must cancel out or balance each other.

Let's analyze each puck one by one:

Puck 1: This puck has two forces acting on it with magnitudes F and 2F. Since the forces are in opposite directions, they have the potential to balance each other if they are equal in magnitude. Therefore, Puck 1 could be in equilibrium if F = 2F.

Puck 2: This puck has two forces acting on it with magnitudes 2F and 3F. Since these forces are in the same direction, they cannot balance each other. Therefore, Puck 2 cannot be in equilibrium.

Puck 3: This puck has three forces acting on it with magnitudes F, 2F, and 3F. These forces are acting in different directions, so they cannot cancel each other out. Therefore, Puck 3 cannot be in equilibrium.

Puck 4: This puck has two forces acting on it with magnitudes 3F and F. Since the forces are in opposite directions, they have the potential to balance each other if they are equal in magnitude. Therefore, Puck 4 could be in equilibrium if F = 3F.

Puck 5: This puck has three forces acting on it with magnitudes 2F, 3F, and F. These forces are acting in different directions, so they cannot cancel each other out. Therefore, Puck 5 cannot be in equilibrium.

Based on the analysis above, Puck 1 and Puck 4 are the two possible pucks that could be in equilibrium. However, only one of them can be in equilibrium. To determine which one, we need additional information about the points of application for each force and their distances from the center of mass of the puck.