A worker drags a box of mass 20 kg across a smooth floor by pulling a rope tied to
To answer your question, I will break it down into steps:
Step 1: Calculate the force of gravity acting on the box:
The force of gravity can be calculated using the formula:
Force of gravity = mass × gravitational acceleration
Given:
Mass of the box (m) = 20 kg
Gravitational acceleration (g) = 9.8 m/s²
Substituting the values into the formula:
Force of gravity = 20 kg × 9.8 m/s² = 196 N
Step 2: Determine the force required to move the box:
The force required to move the box is equal to the force of friction acting on it. This force can be calculated using the equation:
Force of friction = coefficient of friction × normal force
Since the floor is smooth, the coefficient of friction is zero (assuming there is no air resistance or other external factors). Therefore, the force of friction is also zero.
Step 3: Calculate the net force on the box:
The net force on the box is the sum of all forces acting on it. In this case, since there is no frictional force, the net force is simply the force applied by the worker.
Net force = Force applied by the worker
Step 4: Determine the acceleration of the box:
Using Newton's second law of motion, we can relate the net force and the acceleration of the box:
Net force = mass × acceleration
Rearranging the formula:
Acceleration = Net force / mass
Substituting the values:
Acceleration = Force applied by the worker / 20 kg
Since we do not have information about the force applied by the worker, we cannot calculate the acceleration in this case.
Therefore, the acceleration resulting from the worker dragging the box across a smooth floor cannot be determined without additional information.
To determine the force required to drag the box, we need to apply Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). In this case, the box is being moved at a constant speed across a smooth floor, so there is no acceleration. This means that the net force acting on the box is zero.
The force required to drag the box can be determined using the equation:
F = m * a
Since there is no acceleration, the net force acting on the box is zero. However, there is another force acting in the opposite direction—the force of friction. The force of friction opposes the motion of the box and must be overcome by the worker to move the box at a constant speed. This force of friction can be expressed as:
Frictional force (Ffriction) = coefficient of friction (μ) * normal force (Fn)
Since the box is being dragged on a smooth floor, the coefficient of friction is very low. Let's assume it is 0.1. The normal force can be considered equal to the weight of the box, which is the mass multiplied by the acceleration due to gravity (g ≈ 9.8 m/s²).
Fn = m * g = 20 kg * 9.8 m/s² = 196 N
Now we can determine the frictional force by multiplying the coefficient of friction by the normal force:
Ffriction = μ * Fn = 0.1 * 196 N = 19.6 N
Therefore, the worker needs to exert a force of at least 19.6 newtons to overcome the force of friction and drag the box across the smooth floor.