Polly is pushing a box to the right across the floor with a force of 30 N. The force of gravity is 8 N, and the normal force is 8 N. Which value could describe the force of friction if Polly could not move the box?
$\leftarrow 30 N$
$\leftarrow 8 N$
$\rightarrow 8 N$
$\rightarrow 30 N$
Answer (1)
The box is not moving, so the net force on it is zero.
The vertical forces (gravity and normal force) are balanced.
The horizontal force applied by Polly (30 N to the right) is balanced by the force of friction.
Therefore, the force of friction is ← 30 N .
Explanation
Understanding the Problem We are given that Polly is pushing a box to the right with a force of 30 N. The force of gravity is 8 N, and the normal force is 8 N. The box does not move. We need to find the force of friction acting on the box.
Net Force Since the box is not moving, the net force on the box must be zero. This means that the forces in the horizontal direction must balance each other, and the forces in the vertical direction must balance each other.
Vertical Forces In the vertical direction, the force of gravity (8 N downwards) is balanced by the normal force (8 N upwards). So, the net force in the vertical direction is zero.
Horizontal Forces In the horizontal direction, Polly is pushing the box to the right with a force of 30 N. Let the force of friction be F f acting to the left. Since the box is not moving, the net force in the horizontal direction must also be zero. Therefore, the force of friction must be equal in magnitude and opposite in direction to the force Polly is applying.
Calculating Friction Force So, we have: F p − F f = 0 where F p is the force Polly applies (30 N) and F f is the force of friction. Therefore, F f = F p = 30 N The force of friction is 30 N to the left.
Final Answer The possible values for the force of friction are: ← 30 N ← 8 N → 8 N → 30 N Since the force of friction is 30 N to the left, the correct answer is ← 30 N .
Examples
Imagine you're trying to push a heavy crate across the floor. If the crate doesn't move, it's because the force you're applying is being perfectly countered by the force of friction between the crate and the floor. This balance of forces is crucial in many everyday situations, such as ensuring a car remains stationary on a hill or preventing objects from sliding off a table. Understanding how friction works helps us design safer and more efficient systems, from braking mechanisms in vehicles to the grip of our shoes on the ground. By analyzing these forces, we can predict and control the motion of objects around us.
