A 10 kg object is moving with a velocity of 3 m/s. What is the total mechanical energy if it is at a height of 5 m?

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Q: A 10 kg object is moving with a velocity of 3 m/s. What is the total mechanical energy if it is at a height of 5 m?

Solution: Total Mechanical Energy = Kinetic Energy + Potential Energy = 0.5 × 10 kg × (3 m/s)² + 10 kg × 9.8 m/s² × 5 m = 45 J + 490 J = 535 J.

Steps: 12

Step 1: Identify the mass of the object, which is 10 kg.
Step 2: Identify the velocity of the object, which is 3 m/s.
Step 3: Identify the height of the object, which is 5 m.
Step 4: Calculate the Kinetic Energy (KE) using the formula KE = 0.5 × mass × velocity².
Step 5: Plug in the values: KE = 0.5 × 10 kg × (3 m/s)².
Step 6: Calculate (3 m/s)², which is 9 m²/s².
Step 7: Multiply: KE = 0.5 × 10 kg × 9 m²/s² = 45 J.
Step 8: Calculate the Potential Energy (PE) using the formula PE = mass × gravity × height.
Step 9: Use the value of gravity as 9.8 m/s²: PE = 10 kg × 9.8 m/s² × 5 m.
Step 10: Multiply: PE = 10 kg × 9.8 m/s² × 5 m = 490 J.
Step 11: Add the Kinetic Energy and Potential Energy to find the Total Mechanical Energy: Total Mechanical Energy = KE + PE.
Step 12: Total Mechanical Energy = 45 J + 490 J = 535 J.