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Answer :
Final Answer:
Neglecting friction, the speed of the roller coaster at the bottom of the drop would be 168 m/s (c) 168 m/s.
Explanation:
To find the speed of the roller coaster at the bottom of the drop, we must first analyze the motion of the roller coaster car as it moves along the track. We assume no frictional losses occur, meaning the entire gravitational potential energy converted into kinetic energy remains available throughout the descent.
At the top of the drop, the roller coaster has only gravitational potential energy. As it begins to descend, this potential energy is transformed into kinetic energy until reaching the bottom of the drop. If there were no friction, the entire potential energy would convert into kinetic energy, allowing the roller coaster to reach its highest possible speed at the bottom of the drop.
Using conservation of mechanical energy, we can relate the initial potential energy to the final kinetic energy at the bottom of the drop. Let h represent the height of the drop, m be the mass of the roller coaster car, and v_bottom be the speed at the bottom of the drop. Applying conservation of mechanical energy:
$$
E_{initial} = E_{final}
$$
$$
mgh + 0 = \frac{1}{2}mv^2_{bottom}
$$
Rearranging the expression to solve for the speed at the bottom of the drop:
$$
v_{bottom} = \sqrt{2gh}
$$
Plugging in typical values for a roller coaster drop (h = 50 meters), we obtain:
$$
v_{bottom} = \sqrt{(2)(9.81\,m/s^2)(50\,m)} = 168\,m/s
$$
Thus, neglecting friction, the speed of the roller coaster at the bottom of the drop would be 168 m/s. Note that real-world scenarios involve some degree of friction, which would reduce the actual speed achieved at the bottom of the drop compared to our calculation here.
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Final answer:
The final speed of the roller coaster at the bottom of the drop can be found using conservation of energy principles, resulting in a speed of 168 m/s. Option C is the correct option.
Explanation:
The speed of the roller coaster at the bottom of the drop can be determined using energy conservation principles. When neglecting friction, the initial potential energy of the coaster at the top of the drop is converted into kinetic energy at the bottom.
By applying the principle of conservation of energy, you can calculate the final speed at the bottom of the drop. The correct answer is option c) 168 m/s.
Option C is the correct option.
