Final answer:
Marvin can lift a rock that weighs up to 3240 pounds using a 5-foot-long crowbar with the fulcrum placed 6 inches from the rock by applying a 180-pound force, calculated using the principle of moments.
Step-by-step explanation:
The question relates to the physical concept of a lever, where Marvin utilizes a crowbar to lift a rock. To determine how heavy a rock he can lift, we use the principle of moments, which states that the force multiplied by its distance from the fulcrum (moment of force) on one side of the lever must equal the weight of the rock multiplied by the distance from the fulcrum (moment of weight) on the other side. Marvin can exert a force of 180 pounds, and the distance from the fulcrum to the point where the force is applied (5 feet minus 6 inches) is 4.5 feet.
Using the equation Moment of force = Moment of weight, we have:
180 pounds x 4.5 feet = Weight of rock x 0.5 feet
Therefore, the weight of the rock that Marvin can lift is calculated as follows:
Weight of rock = (180 pounds x 4.5 feet) / 0.5 feet
Weight of rock = 1620 pounds / 0.5 feet = 3240 pounds
Marvin can lift a rock that weighs up to 3240 pounds using the crowbar with the given parameters.