consider two solid cones made from a uniform material. The smaller cone is a ½ scale model of the bigger one. They are released from equal height, quickly reach their terminal velocities and fall in air until they hit the ground. Use scaling reasoning to predict which cone will reach the ground first
I know if air resistance is ignored it will be at the same time.
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To predict which cone will reach the ground first, we can use scaling reasoning while considering air resistance.
First, let's define the scaling factor between the smaller cone and the larger cone. Since the smaller cone is a ½ scale model of the bigger one, we can assume that all linear dimensions, such as height and radius, are reduced by a factor of ½.
Now, let's consider the effect of air resistance on the cones as they fall. The larger cone will experience a greater drag force due to its larger surface area compared to the smaller cone. This is because the drag force is proportional to the cross-sectional area of the object.
Since the larger cone has a greater surface area, it will experience a stronger drag force, which will slow it down more than the smaller cone. As a result, the larger cone will take longer to reach its terminal velocity.
On the other hand, the smaller cone will have a smaller surface area and thus experience less drag. This means it will reach its terminal velocity more quickly.
Therefore, taking into account both scaling reasoning and the effect of air resistance, we can predict that the smaller cone will reach the ground first.