Question

Help (give lots of detail)

(a) Which of the graphs shown above correctly models the velocity of disk A as a function of position as it is being pushed by the force? Justify your answer.

(b) After sliding across the horizontal portion of the track, both disks slide partway up the curved section of the track. Identify which disk, if either, reaches a greater maximum height. If both disks reach the same maximum height, state this explicitly.

(c) In a clear, coherent paragraph-length response, justify your answer to part (b).

(d) Consider the case where friction is not negligible and the coefficient of kinetic friction between each disk and the track is the same. The disks are again pushed by the same force over the same distance, and each disk slides partway up the ramp. Identify which disk, if either, would reach a greater maximum height than the other in this case. If both disks reach the same maximum height in this case, state this explicitly. Briefly justify your answer.

Answer 1

The physics questions involve analyzing forces, motion, and energy, such as the maximum heights reached by objects under the influence of forces, and require understanding of Newton's laws, conservation of energy, and dynamics of motion.

Step-by-step explanation:

The questions presented are concerned with physics concepts relating to forces, motion, energy, and the effects of friction. Particularly, these problems deal with the application of Newton's laws, the conservation of energy, and the dynamics of objects in different scenarios including objects being pushed by forces, motions of launchers and projectiles, and skiers on slopes.

For example, when discussing which disk reaches a greater maximum height after being pushed by a force and sliding up a curved track, conservation of mechanical energy principles is essential. That is, the kinetic energy transformed to potential energy will determine the height each disk reaches. Similarly, when assessing the velocity of objects moving up inclines or the effects of gravity and friction, physics fundamentals like kinematic equations and energy transformations are applied.

Moreover, the evaluation of experimental data to validate or invalidate suggested equations is another aspect of these problems. Students must apply their knowledge of physics principles, such as the work-energy theorem and projectile motion equations, to assess the accuracy and consistency of these equations with experimentally observed phenomena.

Answer 2

a) The graph labeled 'Disk A' correctly models the velocity of disk A as a function of position as it is being pushed by the force. This is because the shape of the graph follows the general pattern of an object accelerating non-uniformly: the slope of the graph increases for the first part up until the middle, at which point it levels off and the velocity eventually reaches a maximum.

b) Neither disk reaches a greater maximum height than the other. Both disks reach the same maximum height when they reach the top of the curved section of the track.

c) When both disks are pushed by the same force over the same distance across the horizontal portion of the track, the same amount of kinetic energy is imparted to each disk. This means that each disk will have the same amount of kinetic energy at the bottom of the curved section of the track, and thus both disks will travel with the same velocity when they reach the top of the curved section of the track. Since kinetic energy is conserved, this implies that both disks will reach the same maximum height when they reach the top of the curved section of the track.

d) In the case where friction is not negligible, the coefficient of kinetic friction between each disk and the track is the same. Since friction introduces an additional force to the system, the disk with the greater coefficient of kinetic friction will lose more kinetic energy as it slides up the ramp. Consequently, this disk will reach a lower maximum height than the disk with the smaller coefficient of kinetic friction.