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Understanding how to calculate mass is an essential skill when solving physics problems involving motion. In the context of centripetal force, mass calculation becomes necessary if you know other parameters like force, velocity, and radius.
In our specific problem, we have a speed skater experiencing a centripetal force while moving in a circle. To find the skater's mass, we use the formula for centripetal force, \( F = \frac{mv^2}{r} \).
By rearranging it, we isolate the mass \( m \), obtaining \( m = \frac{Fr}{v^2} \).
Here:

• \( F \) is the centripetal force acting on the body.
• \( v \) is the velocity or speed.
• \( r \) is the radius of the circle.

This formula helps us directly calculate mass from the given values, making it straightforward to understand how changes in speed, force, or the circular path radius can influence the mass determination.

Circular motion is a fascinating concept seen in everyday life, from cars turning around a corner to planets orbiting stars. Understanding it involves various aspects, including speed, radius, and centripetal force.
When an object moves in a circle, it constantly changes direction, even if its speed remains constant. This change in direction is due to centripetal force, which acts towards the center of the circle, keeping the object in its path. For instance, our speed skater maintains circular motion due to the centripetal force applied towards the center of their turn.
Important aspects when considering circular motion:

• Radius \( r \): The distance from the center to the path of motion.
• Velocity \( v \): The speed of the object along the path.
• Centripetal Force \( F \): The net force causing the inward acceleration.

Understanding these factors and how they interrelate supports broader comprehension of any object following a curved path.

Solving physics problems can sometimes feel tricky but becomes manageable with a structured approach. Breaking down a problem into digestible parts, like identifying what is known and what you need to find, is essential.
In our exercise, we dissect the situation by:

• Identifying the given values: radius \( r = 31 \) meters, speed \( v = 14 \) meters per second, and centripetal force \( F = 460 \) Newtons.
• Recognizing the wanted value: the mass of the skater.
• Using the appropriate formula: for centripetal force to express mass in terms of accessible variables.
• Executing the calculation: substituting the known values into the rearranged formula \( m = \frac{Fr}{v^2} \).

This structured method enhances accuracy and confidence in tackling physics problems. As we solve the particular problem, we can see how fundamental each step is for reaching the correct answer of approximately 72.6 kg for the skater's mass.