A worker of a moving company places a 308 kg trunk on a piece of carpeting and slides it across the floor at a constant velocity by exerting a horizontal force of 425 N on the trunk. What horizontal force must the mover apply to move the trunk at a constant rate?
Typo???
You said the answer, 425 Newtons
Something missing in this problem statement? For example the mu of the floor with no carpet?
the mu is .14, sorry!
To move the trunk at a constant velocity, the horizontal force applied by the mover must overcome the force of friction acting on the trunk.
The force of friction can be calculated using the formula:
\(F_{\text{friction}} = \text{coefficient of friction} \times F_{\text{normal}}\)
where \(F_{\text{normal}}\) is the normal force and is equal to the weight of the trunk, and the coefficient of friction is a constant value depending on the surfaces in contact.
In this case, there is no vertical motion, so the normal force is equal to the weight of the trunk, which can be calculated as:
\(F_{\text{normal}} = m \times g\)
where m is the mass of the trunk (308 kg) and g is the acceleration due to gravity (9.8 m/s^2).
\(F_{\text{normal}} = 308 \ \text{kg} \times 9.8 \ \text{m/s}^2 = 3014.4 \ \text{N}\)
Now, we need to find the coefficient of friction. Since the trunk is being placed on a piece of carpeting, we assume a typical value for the coefficient of friction between carpet and the trunk, which is around 0.6.
Using these values, we can calculate the force of friction:
\(F_{\text{friction}} = 0.6 \times 3014.4 \ \text{N} = 1808.64 \ \text{N}\)
To move the trunk at a constant velocity, the horizontal force applied by the mover must be equal and opposite to the force of friction. Therefore, the horizontal force the mover must apply is 1808.64 N.
To find the horizontal force that the mover must apply to move the trunk at a constant rate, we need to consider Newton's first law of motion, which states that an object will remain at rest or move at a constant velocity in a straight line unless acted upon by an external force.
In this case, the trunk is moving at a constant velocity, indicating that the net force acting on it is zero. Therefore, the force applied by the mover must exactly cancel out the opposing forces acting on the trunk.
Here's how to calculate the horizontal force:
1. Identify the forces acting on the trunk:
- Force applied by the mover (unknown)
- Force of friction (opposing the motion of the trunk)
2. Determine the force of friction:
The force of friction can be calculated using the equation:
Force of friction = coefficient of friction × normal force
Since the trunk is placed on a piece of carpeting and is not in contact with any other surface (assuming horizontal movement), the normal force acting on the trunk is equal to its weight,
Normal force = mass × gravitational acceleration
Normal force = 308 kg × 9.8 m/s²
The coefficient of friction between the trunk and the carpeting is not given in the question. Without this information, we cannot calculate the exact force of friction. However, we can assume that the coefficient of friction is such that the trunk can be moved at a constant velocity with the applied force of 425 N.
3. Determine the force applied by the mover:
Since the trunk is moving at a constant velocity, the force applied by the mover must balance out the force of friction, resulting in a net force of zero.
Force applied by the mover = Force of friction
Therefore, the force applied by the mover is 425 N (as given in the question).
So, to move the trunk at a constant rate, the mover must apply a horizontal force of 425 N.