Answer:
The amount of work done to move the 10 kg block at a constant velocity over a distance of 10 m with a 200 N force at an angle of 45 degrees to the horizontal is approximately 1414.2 Joules.
Step-by-step explanation:
To determine the amount of work done, we can use the formula for work:
Work (W) = Force (F) × Distance (d) × cos(θ),
where:
Force (F) is the applied force,
Distance (d) is the distance the object is moved, and
θ (theta) is the angle between the applied force and the direction of motion.
Given:
Force (F) = 200 N
Distance (d) = 10 m
Angle (θ) = 45 degrees
We first need to convert the angle from degrees to radians, as trigonometric functions in most programming languages use radians:
θ (in radians) = 45 degrees × (π/180 degrees)
θ (in radians) = 45 × (π/180) ≈ 0.7854 radians
Now, we can calculate the amount of work done:
Work (W) = 200 N × 10 m × cos(0.7854)
Using a calculator:
Work (W) ≈ 200 N × 10 m × 0.7071
Work (W) ≈ 1414.2 Joules
So, the amount of work done to move the 10 kg block at a constant velocity over a distance of 10 m with a 200 N force at an angle of 45 degrees to the horizontal is approximately 1414.2 Joules.