91Ó°ÊÓ

Friction is a force that opposes the motion of objects in contact. In the given problem, it acts between the box and the floor as the box is being pulled by the rope. Frictional force is calculated as the product of the coefficient of friction and the normal force. However, in this exercise, it is directly provided as 1 N. It acts along the same line as the direction of motion but opposite in sense. This is why, when calculating the work done by friction using the equation \[ W = F \cdot s \cdot \cos(\theta) \] we use \( \theta = 180^\circ \). Remember that \( \cos(180^\circ) = -1 \), which results in negative work, showing that friction takes energy away from the system.When objects move and friction acts on them, energy is spent mainly to overcome this resistance. In our example,

• The work done by friction is \(-1.5 \, \text{J}\).
• It converts mechanical energy, which could have been used for movement, into heat energy.
• The negative sign in work indicates an energy loss due to friction.

Understanding friction's impact is crucial for calculating net work and analyzing energy expenditure in a system.

Tension is the force that is transmitted through the rope in our exercise. This force is responsible for pulling the box along the floor. Since the tension force is not acting purely horizontally but at an angle, a component of this force acts in the direction of pull.When solving for work done by tension, we use the formula:\[ W = F \cdot s \cdot \cos(\theta) \]Here, \( F \) is the tension force (5 N), \( s \) is the displacement (1.5 m), and \( \theta \) is the angle between the force and the direction of displacement (30°). The use of trigonometric functions allows us to accurately reflect the component of force in the actual path of movement. Thus,

• \( \cos(30^\circ) \approx 0.866 \)
• Work done by tension calculates to \( 6.495 \, \text{J} \)

The positive value indicates that the tension is contributing energy to the system, making the box move along the floor.Understanding tension is essential for any system involving ropes, strings, or cables, as it defines the force exerted across these mediums.

Normal force is a contact force that acts perpendicular to surfaces in contact, such as between the box and the floor. In the context of our problem, the normal force solely balances out the weight of the box under the influence of gravity.Since the normal force is perpendicular to the direction of the box's movement,

• The angle \( \theta \) between the normal force and the path of displacement is \( 90^\circ \).
• This leads to a work done calculation of \( W = F \cdot s \cdot \cos(90^\circ) \), which is zero because \( \cos(90^\circ) = 0 \).
• Thus, no work is done by the normal force.

This illustrates a key point: even though forces can be present, not all forces do work. Understanding the role of normal force helps in analyzing motion, especially when surfaces are inclined or curved.

Physics problem solving involves breaking down complex problems into manageable steps. In exercises like these, it's critical to identify each force acting on the system and understand its orientation with respect to the motion.The key steps in problem solving include:

• Identifying all forces involved and the nature of each force (tension, friction, gravity, normal force).
• Understanding direction: analyzing angles and directions between forces and displacement, as this impacts the work calculation through the cosine of the angle.
• Using systematic calculations: applying formulas correctly, such as \( W = F \cdot s \cdot \cos(\theta) \), to find the work done by different forces.
• Putting it all together: summing the work of individual forces to determine total work done, revealing the net effect on the object.

Developing these skills enables thorough analysis and comprehension, not just for solving textbook exercises, but also real-life physical problems.