A force of 15 N is applied at an angle of 30° to the horizontal while moving an

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Question: A force of 15 N is applied at an angle of 30° to the horizontal while moving an object 4 m. What is the work done by the force?

Options:

Correct Answer: 90 J

Solution:

Work done = F × d × cos(θ) = 15 N × 4 m × cos(30°) = 15 N × 4 m × (√3/2) = 60 J.

A force of 15 N is applied at an angle of 30° to the horizontal while moving an object 4 m. What is the work done by the force?

A force of 15 N is applied at an angle of 30° to the horizontal while moving an object 4 m. What is the work done by the force?

Step 1: Identify the force applied, which is 15 N.
Step 2: Identify the distance moved by the object, which is 4 m.
Step 3: Identify the angle of the force with respect to the horizontal, which is 30°.
Step 4: Use the formula for work done: Work = Force × Distance × cos(Angle).
Step 5: Substitute the values into the formula: Work = 15 N × 4 m × cos(30°).
Step 6: Calculate cos(30°), which is √3/2.
Step 7: Substitute cos(30°) into the formula: Work = 15 N × 4 m × (√3/2).
Step 8: Calculate the multiplication: 15 N × 4 m = 60 N·m.
Step 9: Now multiply 60 N·m by (√3/2) to find the work done.
Step 10: The final answer for work done is approximately 60 J.

Work Done – Work is calculated as the product of the force applied, the distance moved in the direction of the force, and the cosine of the angle between the force and the direction of motion.
Trigonometry in Physics – Understanding how to apply trigonometric functions, specifically cosine, to resolve forces into their components.