Final answer:
To calculate work input in Joules for a box pushed up a ramp, convert ft to meters and lb to newtons, then use the equation W = F x d with the effort force and ramp length to find work.
Step-by-step explanation:
To calculate the work input in Joules for pushing a box up an inclined plane, one must first convert all units to the SI (International System of Units). For length, 1 foot (ft) is equal to 0.3048 meters (m), and for weight, 1 pound (lb) is equal to 4.44822 newtons (N).
a) Conversion of units:
- Ramp: 8.5 ft x 0.3048 m/ft = 2.5918 m
- Weight of the box: 50 lb x 4.44822 N/lb = 222.411 N
- Effort: 28 lb x 4.44822 N/lb = 124.55016 N
b) Calculation of work input in Joules:
Work input (W) is the force applied (F) times the distance moved by the force (d), W = F x d. Here the force is the effort applied, and the distance is the length of the ramp.
W = 124.55016 N x 2.5918 m = 322.79223488 J
c) Application of inclined plane principles:
When a box is pushed up a ramp, an inclined plane reduces the effort needed to lift it vertically by extending the distance over which the force is applied, allowing the box to be moved with less force than lifting it straight up.