If a 3 kg object is moving with a speed of 4 m/s, what is the total mechanical energy if it is at a height of 2 m?

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Q: If a 3 kg object is moving with a speed of 4 m/s, what is the total mechanical energy if it is at a height of 2 m?

Solution: Total mechanical energy = K.E + P.E = 0.5 × 3 kg × (4 m/s)² + 3 kg × 9.8 m/s² × 2 m = 24 J + 58.8 J = 82.8 J.

Steps: 13

Step 1: Identify the mass of the object. The mass is 3 kg.
Step 2: Identify the speed of the object. The speed is 4 m/s.
Step 3: Identify the height of the object. The height is 2 m.
Step 4: Calculate the Kinetic Energy (K.E) using the formula K.E = 0.5 × mass × speed².
Step 5: Substitute the values into the K.E formula: K.E = 0.5 × 3 kg × (4 m/s)².
Step 6: Calculate (4 m/s)², which is 16 m²/s².
Step 7: Multiply: K.E = 0.5 × 3 kg × 16 m²/s² = 24 J.
Step 8: Calculate the Potential Energy (P.E) using the formula P.E = mass × gravity × height.
Step 9: Use the value of gravity as 9.8 m/s². Substitute the values into the P.E formula: P.E = 3 kg × 9.8 m/s² × 2 m.
Step 10: Multiply: P.E = 3 kg × 9.8 m/s² × 2 m = 58.8 J.
Step 11: Add the K.E and P.E to find the total mechanical energy: Total mechanical energy = K.E + P.E.
Step 12: Substitute the values: Total mechanical energy = 24 J + 58.8 J.
Step 13: Calculate the total: Total mechanical energy = 82.8 J.