Chapter 6: Problem 7
You slide a 0.12-kg coffee mug
Short Answer
Expert verified
The work done on the mug is 0.00617 J.
Step by step solution
01
Understand the Problem
We need to find the work done on the coffee mug as it slides across the table. Work is defined as the force exerted on an object times the distance the object moves in the direction of the force. Mathematically, where is the force, is the distance, and is the angle between the force and the motion's direction.
02
Calculate the Net Force
First, we need to determine the net force acting on the mug. The net force was exerted minus kinetic friction force. The force of friction, , is given by , where is the coefficient of kinetic friction, and is the normal force. Since the mug is on a horizontal surface, (weight of the mug).
03
Calculate Normal Force
The normal force is calculated as following:
04
Calculate Friction Force
Now, calculate the friction force, using:
05
Calculate Net Force
The net force, , is the applied force minus the friction force:
06
Calculate the Work Done
With the net force calculated, now use the work formula. Since the force direction and motion direction are the same, degrees. Thus, :
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Kinetic Friction
When an object slides across a surface, kinetic friction is the force opposing the motion. It's what slows down the coffee mug as it moves across the table. Kinetic friction depends on two things:
, indicating relatively low friction between the mug and the table.
To find the kinetic friction force, use the formula , where is the kinetic friction force, is the coefficient, and is the normal force.
- The nature of the surfaces in contact, represented by the coefficient of kinetic friction,
. - The normal force acting on the object.
To find the kinetic friction force, use the formula
Normal Force
The normal force is crucial in understanding how objects interact on surfaces. It acts perpendicular to the surface and supports the weight of an object resting on it. For our coffee mug, the normal force is equal to the weight of the mug since it is on a horizontal surface and there's no vertical acceleration. Thus, we use the formula , where is the mass and is the acceleration due to gravity, which is approximately 9.81 m/s².
- In our example,
. - This normal force serves as a basis for calculating kinetic friction.
Net Force
Net force is the total force acting on an object after all individual forces are combined. Calculating net force is vital to determine how an object moves. For the coffee mug, the net force is the force you exert minus the kinetic friction force.
First, calculate the exerted force minus the friction force:
If more force were applied or if friction were lower, the net force would increase, making the mug move faster.
First, calculate the exerted force minus the friction force:
- Applied Force = 0.10 N
- Friction Force = 0.05886 N
- Net Force,
If more force were applied or if friction were lower, the net force would increase, making the mug move faster.
Work Formula
The work done on an object is the transfer of energy as a result of the force applied to move it. The amount of work depends on three main factors: . In our scenario, since the force direction and the mug's motion direction are the same, the angle is 0, making .
Plugging in the values from earlier:
- The force applied (
. - The distance the object moves in the direction of the force (
. - The angle between the force applied and the direction of movement, noted as
.
Plugging in the values from earlier:
- Net Force = 0.04114 N
- Distance = 0.15 m
- Work,