Question

A moving company collects data about couches they move and displays the data in a table. The force along the ramp, the angle of the ramp, and the height the couch is raised from the ground to the platform is shown below.

A 4 column table with 3 rows. The first column is labeled couch with entries 1, 2, 3. The second column is labeled force in newtons with entries 450, 475 and 450. The third column is labeled angle of degrees above the horizontal with entries 25, 30 and 35. The last column is labeled height in meters with entries 12, 15 , 15.
Which statements correctly compare the work done to move the couches? Select three options.

The same amount of work is done for couches 1 and 3.
The same amount of work is done for couches 2 and 3.
The work for couch 1 is greater than the work for couch 2.
The work for couch 2 is less than the work for couch 3.
The work for couch 3 is greater than the work for couch 1.
The work for couch 2 is greater than the work for couch 1.

Answer 1

Work done by the applied force along the ramp = F × distance along ramp. The ramp distance s = height / sin(angle), so
W = F · h / sin(θ).

Compute each:
- Couch 1: W1 = 450·12 / sin25° ≈ 5400 / 0.42262 ≈ 1.278×10^4 J
- Couch 2: W2 = 475·15 / sin30° = 7125 / 0.5 = 1.425×10^4 J
- Couch 3: W3 = 450·15 / sin35° ≈ 6750 / 0.57358 ≈ 1.177×10^4 J

Ordering: W2 > W1 > W3.

So only this statement is correct:
- The work for couch 2 is greater than the work for couch 1.

All the other listed statements are false. (There are not three correct choices.)