Question

Audrey is moving furniture in her house, including a 30 kg treasure chest.
She is applying a force of 25 N to the left, overcoming 10 N of friction to
accelerate the treasure chest.
1. Are the forces balanced in the Y Direction? YES or NO (circle one)
2. Are the forces balanced in the X Direction? YES or NO (circle one)
3. What is the net force being applied to the treasure chest?

Answer 1

Answer:

Forces in the vertical Y direction are balanced, assuming that the floor is level.

Forces in the horizontal X direction are not balanced.

The net force would be $15\; {\rm N}$ to the left, assuming that the object was not moving until Audrey applied the force.

Explanation:

Assume that the floor is level. Forces on the object in the vertical Y direction would be:

• Weight (downward.)
• Normal force from the ground (upward.)

If the floor is level and the object is moving along the floor, there would no motion in the vertical direction. Since the vertical component of acceleration would then be $0$, the vertical component of net force would also be $0\!$.

Thus, forces would be balanced in the vertical Y direction.

The question states that the force Audrey exerted points to the left. In other words, this $25\; {\rm N}$ force is entirely horizontal. Assuming that the object wasn't moving until Audrey exerted this force to the left, friction would resist the motion and would point in the opposite direction- to the right.

Under these assumptions, forces on the object in the horizontal X direction would include:

• $25\; {\rm N}$ force to the left, and
• $10\; {\rm N}$ friction to the right.

Thus, the forces in the horizontal X direction are not balanced.

Take the vector sum of all forces on this object to find the net force. Forces in the vertical direction are already balanced. In the horizontal direction, since the two forces are in opposite directions, magnitude of the resultant force would be the difference between that of these two forces:

$25\; {\rm N} - 10\; {\rm N} = 15\; {\rm N}$.

The magnitude of the external force from Audrey ($25\; {\rm N}$) exceeds that of friction ($10\; {\rm N}$.) Since these two forces are in opposite directions, the resultant force would be in the same direction as the force with the larger magnitude- the force from Audrey. Thus, the net force on the object would point to the left.