To determine the total work done in moving the crate, we need to calculate the work done in each segment of the movement - dragging along the smooth floor, pulling up the ramp, and dragging along the level platform.
1. Work done while dragging along the smooth floor:
The formula for work is given by W = Fd cosθ, where W represents work done, F is the force applied, d is the displacement, and θ is the angle between the force and displacement vectors. In this case, the force applied is 30 N and the displacement is 3 meters. The angle between the force and displacement vectors can be found using trigonometry as cosθ = cos(180° - θ). Since the force is applied at 25° to the floor, the angle between the force and displacement vectors is 180° - 25° = 155°. Plugging the values into the formula, we have:
W1 = 30 N * 3 m * cos(155°)
2. Work done while pulling up the ramp:
Similar to the first step, we use the formula W = Fd cosθ. The force and displacement remain the same at 30 N and 4 meters, respectively. The angle between the force and displacement vectors is 90° - 20° = 70°. Applying the formula, we get:
W2 = 30 N * 4 m * cos(70°)
3. Work done while dragging along the level platform:
Again, using the formula W = Fd cosθ, the force and displacement remain the same (30 N and 5 meters). The angle between the force and displacement vectors is 0° since they are parallel. Thus, the angle of cosθ is 0°, and we have:
W3 = 30 N * 5 m * cos(0°)
Now, to find the total work done, we simply sum up the work done in each segment:
Total work done = W1 + W2 + W3
Note that the cosine function can be evaluated using a scientific calculator or trigonometric tables.