Chapter 6: Problem 7
You slide a 0.12-kg coffee mug 0.15 m across a table. The force you exert is horizontal and of magnitude 0.10 N. The coefficient of kinetic friction between the mug and the table is 0.05. How much work is done on the mug?
Short Answer
Expert verified
0.00618 J of work is done on the mug.
Step by step solution
01
Identify Forces and Parameters
To solve for the work done on the coffee mug, first identify the forces acting on it. We have a horizontal applied force of 0.10 N, the mass of the mug is 0.12 kg, the displacement is 0.15 m, and the coefficient of kinetic friction between the mug and the table is 0.05.
02
Calculate Normal Force
The normal force () is equal to the gravitational force acting on the mug, which is given by the formula: \( F_{n} = m \cdot g \). Substituting the values, we have:\[ F_{n} = 0.12 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 1.176 \, \text{N} \]
03
Calculate Frictional Force
The frictional force () is calculated using the formula: \( F_{f} = \mu \, \cdot F_{n} \), where \( \mu \) is the coefficient of kinetic friction. Substituting the given values, we have:\[ F_{f} = 0.05 \times 1.176 \, \text{N} = 0.0588 \, \text{N} \]
04
Net Force Calculation
The net force () acting on the mug is the applied force minus the frictional force:\[ F_{ ext{net}} = F_{ ext{applied}} - F_{f} = 0.10 \, \text{N} - 0.0588 \, \text{N} = 0.0412 \, \text{N} \]
05
Calculate Work Done
The work done () on the mug is given by the formula: \( W = F_{ ext{net}} \cdot d \), where \( d \) is the displacement. Substituting the calculated net force and displacement, we have:\[ W = 0.0412 \, \text{N} \times 0.15 \, \text{m} = 0.00618 \, \text{J} \]
06
Conclusion
Finally, the work done on the coffee mug by the net force is 0.00618 Joules.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Kinetic Friction
Kinetic friction is the force that opposes the motion of two surfaces sliding past each other. It is crucial in determining how much work needs to be done to move an object. Whenever surfaces are in motion relative to each other, kinetic friction comes into play. This force depends on two main factors: the normal force and the coefficient of kinetic friction.
In our example with the coffee mug, the kinetic frictional force is calculated using the formula:
In our example with the coffee mug, the kinetic frictional force is calculated using the formula:
- \( F_{f} = \mu \cdot F_{n} \)
Normal Force
The normal force is an essential concept in physics, particularly when analyzing forces on a surface. It is the perpendicular force exerted by a surface to support the weight of an object resting on it. For objects laid flat on a horizontal surface, like our coffee mug, the normal force balances the gravitational force. This balance prevents objects from accelerating into the surface.
The normal force can be calculated using:
The normal force can be calculated using:
- \( F_{n} = m \times g \)
Net Force
The net force is the total force acting on an object. It is the vector sum of all the individual forces applied to that object. Understanding net force helps us determine the motion of an object, like whether it will accelerate, decelerate, or move at a constant speed.
In the case of the sliding coffee mug, the net force is the result of subtracting the frictional force from the applied force:
In the case of the sliding coffee mug, the net force is the result of subtracting the frictional force from the applied force:
- \( F_{\text{net}} = F_{\text{applied}} - F_{f} = 0.10 \, \text{N} - 0.0588 \, \text{N} \)
Displacement
Displacement refers to the change in position of an object. It is a vector quantity, meaning it has both magnitude and direction. In physics, displacement is crucial for calculating work done on an object, which is the energy transferred when a force moves an object over a distance.
In the case of our coffee mug, the displacement is 0.15 m. This is the measure of how far the mug moved across the table. When calculating work, we use this distance alongside the net force:
In the case of our coffee mug, the displacement is 0.15 m. This is the measure of how far the mug moved across the table. When calculating work, we use this distance alongside the net force:
- \( W = F_{\text{net}} \cdot d \)
Gravitational Force
Gravitational force is a fundamental force in physics, responsible for attracting objects with mass towards each other. On Earth, it gives weight to objects, pulling them toward the center of the planet. This force is what holds the coffee mug on the table. Without it, objects would float away.
The gravitational force acting on any object with mass can be calculated using:
The gravitational force acting on any object with mass can be calculated using:
- \( F_{g} = m \times g \)