Question

Why does a bicyclist pick up speed on a downhill road even when he is not pedaling? Does this violate the conservation of energy principle?

Short answer

Answer: A bicyclist picks up speed on a downhill road due to the conversion of gravitational potential energy into kinetic energy. As the bicyclist's height above the ground decreases, their potential energy decreases, and the lost potential energy is converted into kinetic energy, causing the bicyclist's velocity to increase. This process does not violate the conservation of energy principle, as the total energy in the system remains constant.

Step-by-step solution

Understanding gravitational potential energy

When an object is at a certain height above the ground, it possesses potential energy due to its position in the gravitational field. This potential energy is called gravitational potential energy, which can be calculated using the formula: PE_gravity = m * g * h, where m is the mass of the object, g is the acceleration due to gravity (approximately 9.81 m/s^2 on Earth), and h is the height of the object above the ground.

Understanding kinetic energy

An object in motion has energy due to its motion, which is called kinetic energy. The kinetic energy of an object can be calculated using the formula: KE = 0.5 * m * v^2, where m is the mass of the object and v is its velocity.

Understanding the conservation of energy principle

The conservation of energy principle states that energy cannot be created or destroyed, only converted from one form to another. In a closed system, the total energy remains constant, which means that if the potential energy of an object decreases, its kinetic energy must increase to keep the total energy constant.

Applying the conservation of energy principle to the bicyclist

When a bicyclist goes downhill, their potential energy decreases because their height above the ground (h) decreases. According to the conservation of energy principle, the lost potential energy must be converted into another form of energy, in this case, kinetic energy. As the potential energy decreases and gets converted to kinetic energy, the velocity of the bicyclist increases. That's why the bicyclist picks up speed on a downhill road, even when they're not pedaling.

Verifying whether this violates the conservation of energy principle

As we saw in step 4 that the lost potential energy is converted into kinetic energy, the total energy remains constant, not violating the conservation of energy principle.

Key concepts

Gravitational Potential Energy

Imagine holding a ball high above the ground. That ball has stored energy just because of its position. This is what we call gravitational potential energy (GPE). It's the energy an object possesses due to its location in a gravitational field, usually relative to the Earth's surface.

The formula for gravitational potential energy is expressed as \( PE_{gravity} = m \times g \times h \), where \(m\) is the mass of the object in kilograms (kg), \(g\) is the acceleration due to gravity which is approximately \(9.81 m/s^2\) on Earth, and \(h\) is the height in meters (m) above ground level. In simpler terms, the higher or heavier an object, the more potential energy it has.

Kinetic Energy

Now, think about a ball rolling across the floor. This energy of motion is called kinetic energy (KE). Any moving object uses kinetic energy to travel from one place to another. The kinetic energy an object has depends on both its mass and its speed.

The equation we use to find the kinetic energy of an object is \( KE = 0.5 \times m \times v^2 \), with \(m\) being the object's mass and \(v\) being its velocity. The faster an object moves, or the more mass it has, the higher its kinetic energy. It's crucial to understand that even when an object seems to be still, it may possess kinetic energy. For instance, the Earth has immense kinetic energy in its rotation, despite us not feeling constant movement.

Energy Conversion

The principle of energy conservation is fundamental to understanding how the world works. It tells us that within a closed system, energy can change forms but can never disappear or appear out of nowhere.

This is what happens when our bicyclist rides downhill without pedaling and picks up speed. The gravitational potential energy, which was high when at the top of the hill, is converted into kinetic energy as height decreases. No energy is lost in this process; it simply changes from one form (potential) to another (kinetic). This concept is evident in many real-life scenarios, such as a roller coaster gaining speed as it descends or a falling apple accelerating towards the ground.

Understanding these forms of energy and their conversion is not only key to physics but is also essential for many aspects of our daily lives, including how we generate and use electricity, the functioning of vehicles, and much more.