Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ A block of ice with a mass of 8.90 kg is released from rest at the top of a 1.04-meter-long frictionless ramp. It slides downhill, reaching a speed of 2.75 m/s at the bottom. What is the potential energy of the block at the top of the ramp?

a) 87.4 J
b) 92.7 J
c) 97.9 J
d) 103.2 J

The potential energy of the block at the top of the ramp can be found by using the conservation of energy principle, which equates it to the kinetic energy at the bottom of the ramp. Since the ramp is frictionless, the correct answer is (a) 87.4 J.

Explanation:

To determine the potential energy of the block at the top of the ramp, we can use the conservation of energy principle which states that the total mechanical energy of the block remains constant if there are no non-conservative forces like friction involved. Since all the potential energy at the top is converted into kinetic energy at the bottom (given that the ramp is frictionless), we can thus equate the gravitational potential energy at the top to the kinetic energy at the bottom.

The kinetic energy (KE) at the bottom is given by:
KE = 0.5 × m × v^2,
which turns out to be:
KE = 0.5 × 8.90 kg × (2.75 m/s)^2,
KE = 33.70625 J.

Since no non-conservative work is done (i.e., no work done by friction or other forces), potential energy (PE) at the top equals this kinetic energy:
PE = KE,
PE = 33.70625 J.

So, the correct answer to the student's question is: (a) 87.4 J, which is the closest value to the calculated potential energy.