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Answer :
Final Answer:
The final speed of the block of ice cream, when it reaches the bottom of the inclined plane, is approximately 5.84 m/s.
Explanation:
To find the final speed of the block of ice cream, we can use the principles of mechanical energy conservation. Since we're ignoring friction in this scenario, the initial mechanical energy of the block is equal to its final mechanical energy. Mechanical energy is the sum of kinetic energy (KE) and potential energy (PE).
At the top of the incline, the block only has potential energy (PE) due to its height above the bottom of the incline. As it slides down, this potential energy is converted into kinetic energy.
The potential energy is given by:
PE = m * g * h,
Where:
- m is the mass of the block (2.00 kg),
- g is the acceleration due to gravity (approximately 9.81 m/s²),
- h is the height (0.750 m).
PE = 2.00 kg * 9.81 m/s² * 0.750 m = 14.71 J.
At the bottom of the incline, all the potential energy has been converted into kinetic energy, so:
PE = KE,
KE = 14.71 J.
The kinetic energy is given by:
KE = ½ * m * v²,
Where:
- m is the mass of the block (2.00 kg),
- v is the final velocity (what we want to find).
Substituting in the known values:
14.71 J = ½ * 2.00 kg * v².
Now, solve for v:
v = √(2 * KE / m) = √(2 * 14.71 J / 2.00 kg) ≈ 5.84 m/s.
Therefore, the final speed of the block of ice cream when it reaches the bottom of the inclined plane is approximately 5.84 m/s.
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