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A 5 kg rigid crate moves from rest down path ABC as shown in the diagram below (diagram not drawn to scale) - NSC Physical Sciences - Question 4 - 2016 - Paper 1
Question 4
A 5 kg rigid crate moves from rest down path ABC as shown in the diagram below (diagram not drawn to scale). Section AB of the path is frictionless whilst section BC... show full transcript
Worked Solution & Example Answer:A 5 kg rigid crate moves from rest down path ABC as shown in the diagram below (diagram not drawn to scale) - NSC Physical Sciences - Question 4 - 2016 - Paper 1
Step 1
4.1 State, in words, the principle of the conservation of mechanical energy.
Answer
The principle of conservation of mechanical energy states that the total mechanical energy of an isolated system remains constant if there are no external forces doing work on the system. This means that the sum of gravitational potential energy and kinetic energy remains the same throughout the motion.
Step 2
4.2 Use the principle of the conservation of mechanical energy to calculate the velocity of the crate when it reaches point B.
Answer
Initially, at point A, the crate is at rest, and all its energy is gravitational potential energy (PE). As it descends to point B, this potential energy is converted into kinetic energy (KE).
Using the formula: where:
- (acceleration due to gravity)
Thus,
At point B, this potential energy becomes kinetic energy: KE_B = rac{1}{2}mv^2 Setting gives:
196.2 = rac{1}{2} imes 5 imes v^2
Solving for :
ightarrow v^2 = 78.48 ightarrow v = ext{ approximately } 8.85 ext{ m/s}$$Step 3
Step 4
Step 5