Final answer:
To expend 1000 food calories, which is equivalent to 4184000 joules, by lifting a 50 kg mass 2 m high (requiring 980 joules per lift), it would take approximately 4271 lifts, which does not match any of the given options in the question.
Step-by-step explanation:
To determine how many times the student must lift a 50 kg mass 2 meters to expend the energy equivalent to a dessert rated at 1000 food calories, we will first convert food calories to joules since 1 food calorie is equivalent to 4184 joules. Therefore, 1000 food calories equals 1000 × 4184 joules = 4184000 joules.
To calculate the energy or work done by lifting an object, we can use the formula: Work (Joules) = Force (Newtons) × Distance (meters). The force required to lift the 50 kg mass is equal to the weight of the mass, given by the gravitational field strength (≈9.8 m/s²) times the mass (50 kg), giving a force of 490 Newtons. Thus, lifting this mass 2 meters would require 490 N × 2 m = 980 joules of energy.
Finally, we divide the total joules required from the dessert by the joules used per lift to find out how many lifts are needed: 4184000 joules / 980 joules per lift ≈ 4271 lifts. However, none of the options provided in the question (192, 48, 96, 24) matches this result. It is important to ensure the calorie to joule conversion is used correctly, as food calories may sometimes be referred to as Calories with an upper case 'C', indicating kilocalories, so if one mistakenly uses the lower case unit (calories), the answer would be far less. In this context, the student may have intended to refer to kilocalories. If one calorie equals 4.184 joules, then 1000 kilocalories would equal to 4,184,000 joules, and the number of lifts would be: 4184000 joules / 980 joules per lift = 4271 lifts.