What is the acceleration, as a multiple of g, if this force is applied to a 110 kg bicyclist? This is the combined mass of the cyclist and the bike.

Verified step by step guidance

1. Step 1: Begin by identifying the given values in the problem. The mass of the bicyclist and bike combined is 110 kg. The force applied is not explicitly stated in the problem, so ensure you have the value of the force from prior context or calculations.
2. Step 2: Recall Newton's Second Law of Motion, which states that \( F = ma \), where \( F \) is the force, \( m \) is the mass, and \( a \) is the acceleration. Rearrange this formula to solve for acceleration: \( a = \frac{F}{m} \).
3. Step 3: Substitute the given values into the formula. Use \( m = 110 \; \text{kg} \) and the force \( F \) (ensure you have the numerical value of \( F \) from the problem context). The acceleration \( a \) can now be calculated as \( a = \frac{F}{110} \).
4. Step 4: To express the acceleration as a multiple of \( g \) (where \( g \approx 9.8 \; \text{m/s}^2 \)), divide the calculated acceleration \( a \) by \( g \). This gives \( a_{\text{multiple}} = \frac{a}{g} = \frac{F}{110 \cdot g} \).
5. Step 5: Ensure the units are consistent throughout the calculation. The force \( F \) should be in newtons (\( \text{N} \)), the mass in kilograms (\( \text{kg} \)), and \( g \) in \( \text{m/s}^2 \). Once the formula is set up, you can calculate the numerical value if needed.

Key Concepts

Newton's Second Law of Motion

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This relationship is expressed by the formula F = ma, where F is the net force, m is the mass, and a is the acceleration. Understanding this law is crucial for calculating the acceleration of the bicyclist when a force is applied.

Gravitational Acceleration (g)

Gravitational acceleration, denoted as g, is the acceleration due to Earth's gravity, approximately 9.81 m/s². When comparing other accelerations to g, we express them as multiples of this value. This concept is essential for understanding how the acceleration of the bicyclist relates to the force applied and how it compares to the force of gravity.

Mass and Weight

Mass is a measure of the amount of matter in an object, typically measured in kilograms, while weight is the force exerted by gravity on that mass. The weight of the bicyclist and bike can be calculated using the formula W = mg, where W is weight, m is mass, and g is gravitational acceleration. Recognizing the distinction between mass and weight is important for applying Newton's Second Law correctly in this context.