A student is trying to reduce the mass of a racing bike to achieve greater acceleration. Which would be more beneficial to reduce (assuming each has identical mass)?
a. decrease mass in the frame
b. decrease mass in the wheels
c. decrease mass in the rider
d. these are all equal
b could help, but the rotational inertia involved is trivial, it hardly could be measured on linear acceleration difference.
Bob is right ... especially if the wheels have the same mass as the other components
it lowers the overall mass of the bike
PLUS
it reduces the peddling effort
a double benefit
If you get this question in your homework, the answer is the tires/wheels. Yes, the increase in linear acceleration wouldn't be that much greater by reducing the mass of the wheels, but it still increases the acceleration by some.
To determine which option would be more beneficial to reduce in order to achieve greater acceleration, let's analyze the principles of physics involved.
The acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. According to Newton's second law of motion, the formula for acceleration (a) is given by the equation:
a = F / m
Where F is the force applied on the object and m is the mass of the object.
Since we want to increase acceleration, we need to decrease mass. Now let's consider each option:
a. decrease mass in the frame: The mass of the bike frame is an essential part of the overall mass of the racing bike. Decreasing the mass of the frame will reduce the total mass of the bike.
b. decrease mass in the wheels: The mass of the wheels also contributes to the overall mass of the bike. By reducing the mass of the wheels, the total mass of the bike decreases.
c. decrease mass in the rider: The rider's mass is additional to the mass of the bike itself. By reducing the rider's mass, the total mass of the system (rider + bike) decreases.
Now, to determine which option would be more beneficial, we need to analyze the impact of reducing each component's mass on the overall mass of the system.
If we assume that the mass reduction in each component (frame, wheels, rider) is equal, then reducing any of these components would result in an equal reduction in the total mass. Therefore, option (d) "these are all equal" would be correct.
However, if we assume we can achieve a greater mass reduction in one component compared to the others, then reducing the mass in that particular component would be more beneficial. For example, if we can significantly reduce the rider's mass compared to the frame or wheels, it would have a greater impact on reducing the overall mass and consequently increasing acceleration.
In summary, if the mass reduction is equal across all components, then option (d) is the correct answer. However, if there is a more significant mass reduction possible in one specific component, then reducing the mass in that component would be more beneficial.