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Chapter 7: Problem 4

Can potential energy be negative? Can kinetic energy? Can total mechanical energy? Explain.

Short Answer

Expert verified
Potential energy can indeed be negative in some systems where a force is required to hold it together. Kinetic energy, however, can never be negative, as it is a result of an object's speed (which cannot be negative) and its mass (which also cannot be negative). Total mechanical energy can be negative if the potential energy is negative and its absolute value is greater than the kinetic energy.

Step by step solution

01

Understanding Potential Energy

Potential energy is the energy that an object has because of its position in relation to other objects. It is usually taken to be zero for a convenient choice of position (like the Earth's surface for gravitational potential energy), but it is completely arbitrary. It can take a negative value if a force is required to hold a system together like in case of gravitational potential energy or the elastic potential energy of a spring.
02

Understanding Kinetic Energy

Kinetic energy is the energy that an object has due to its motion. The formula for kinetic energy is \( \frac{1}{2}mv^2 \), where m is the mass and v is the speed of the object. Since both mass and speed are always positive or zero, the kinetic energy of an object can never be negative.
03

Understanding Total Mechanical Energy

The total mechanical energy of a system is the sum of its kinetic and potential energies. It can be negative if the potential energy of the system is negative and its absolute value is greater than the kinetic energy. However, in most of the systems, it's usually positive or zero.

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