91Ó°ÊÓ

The work-energy principle is a fundamental concept in physics. It says that the work done on an object is equal to the change in its kinetic energy. This principle is crucial when analyzing situations where forces cause motion changes, such as stopping a car. Changing an object’s velocity requires work, either adding energy to make it move faster or removing energy to slow it down. In this exercise, the work done to stop the car equals its initial kinetic energy before coming to rest. Since the car stops, the final kinetic energy is zero, and the work done is thus equal to the negative of its initial kinetic energy. This is important because it aligns with the fact that energy doesn’t disappear but transforms from kinetic energy to other forms, like heat due to friction. The equation used is:

• Work done \[ W = - KE_{initial} \]
• The negative sign indicates work is done against the car’s motion.

Remember, a negative work value simply indicates the direction relative to the force applied. Here, the magnitude of work indicates the total energy required to stop the car. Overall, the work-energy principle helps understand energy transfer during motion.

Velocity conversion is essential in physics as it ensures calculations are performed in consistent units. For this exercise, we convert the car's speed from kilometers per hour (km/h) to meters per second (m/s). The standard conversion factor is:

• 1 km/h = \[ \frac{1}{3.6} \] m/s

This conversion is crucial because many physics formulas, particularly those involving kinetic energy, require measurements in the metric system's standard units, including m/s for velocity. To convert 95 km/h to m/s:

• Multiply 95 by \( \frac{1}{3.6} \) to get \( 26.39 \) m/s.

This provides an accurate speed in m/s, ensuring calculations like kinetic energy or work done are correct. Misalignment of units can lead to significant computational errors. Always check units when dealing with physics problems to ensure all aspects of the calculation are consistent.

Kilograms to Joules conversion is not direct because they measure different things. Kilograms (kg) represent mass, while Joules (J) represent energy. In physics, we often relate mass to energy using the kinetic energy formula,

• \[ KE = \frac{1}{2} mv^2 \]
• \(m\) is in kilograms, and \(v\) is in meters per second.

To find kinetic energy in Joules:

• Use the mass of the object and its velocity to calculate kinetic energy.
• Calculate with: \( KE = \frac{1}{2} \times 1300 \times (26.39)^2 = 452645.45 \) Joules

This equation shows how mass and velocity interact to produce energy, expressed in Joules. It’s important to do this conversion correctly, as it directly impacts the energy-related calculations required to solve the problem. Understanding the relationship between mass, velocity, and energy crucially links different units into practical applications such as determining the work needed to stop a moving object.