Question

An electric hoist does 75,845 J of work in raising a 82 kg load. How high (in meters) was the load lifted? (Give the answer without units and round it to the nearest whole number.)

Answer 1

The 82 kg load was lifted approximately 94 meters high by an electric hoist that did 75,845 J of work, calculated using the work done against the gravity formula.

Step-by-step explanation:

To figure out how high an 82 kg load was lifted by an electric hoist that did 75,845 J of work, we use the formula for work done against gravity, which is work (W) = force (F) × distance (h), where the force here is weight, calculated by the equation F = mass (m) × gravity (g). Plugging in the values, we have:

W = m × g × h,

Where:

W is the work done (75,845 J),

m is the mass of the load (82 kg),

g is the acceleration due to gravity (9.8 m/s2), and

h is the height the load was lifted.

Rearranging the equation for h gives us:

h = W / (m × g)

Substituting the known values, we get:

h = 75,845 J / (82 kg × 9.8 m/s2)

h ≈ 94.39 m

So, rounding to the nearest whole number, the load was lifted approximately 94 meters high.

The load was lifted to a height of approximately 94 meters, as calculated using the work-energy principle. This calculation provides insight into the vertical displacement achieved by the electric hoist in performing the specified amount of work.