A 4 kg object is moving with a speed of 5 m/s. What is the total mechanical ener

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Question: A 4 kg object is moving with a speed of 5 m/s. What is the total mechanical energy if it is at a height of 2 m?

Options:

Correct Answer: 70 J

Solution:

Total mechanical energy = Kinetic energy + Potential energy = 0.5 × 4 kg × (5 m/s)² + 4 kg × 9.8 m/s² × 2 m = 50 J + 78.4 J = 128.4 J.

A 4 kg object is moving with a speed of 5 m/s. What is the total mechanical energy if it is at a height of 2 m?

A 4 kg object is moving with a speed of 5 m/s. What is the total mechanical energy if it is at a height of 2 m?

Step 1: Identify the mass of the object, which is 4 kg.
Step 2: Identify the speed of the object, which is 5 m/s.
Step 3: Identify the height of the object, which is 2 m.
Step 4: Calculate the kinetic energy using the formula: Kinetic Energy = 0.5 × mass × (speed)².
Step 5: Substitute the values into the kinetic energy formula: Kinetic Energy = 0.5 × 4 kg × (5 m/s)².
Step 6: Calculate (5 m/s)², which is 25 m²/s².
Step 7: Multiply: 0.5 × 4 kg × 25 m²/s² = 50 J. This is the kinetic energy.
Step 8: Calculate the potential energy using the formula: Potential Energy = mass × gravity × height.
Step 9: Use the value of gravity as approximately 9.8 m/s².
Step 10: Substitute the values into the potential energy formula: Potential Energy = 4 kg × 9.8 m/s² × 2 m.
Step 11: Multiply: 4 kg × 9.8 m/s² = 39.2 kg·m/s² (which is the same as 39.2 N).
Step 12: Now multiply by height: 39.2 N × 2 m = 78.4 J. This is the potential energy.
Step 13: Add the kinetic energy and potential energy to find the total mechanical energy: Total Mechanical Energy = Kinetic Energy + Potential Energy.
Step 14: Substitute the values: Total Mechanical Energy = 50 J + 78.4 J.
Step 15: Calculate the total: 50 J + 78.4 J = 128.4 J.

Kinetic Energy – The energy an object possesses due to its motion, calculated as 0.5 × mass × velocity².
Potential Energy – The energy an object possesses due to its position in a gravitational field, calculated as mass × gravitational acceleration × height.
Total Mechanical Energy – The sum of kinetic and potential energy in a system.