CONCEPTUAL Physics PRACTICE PAGE Chapter 4 Newton's Second Law of Motion Converting Mass to Weight Objects with mass also have weight (although they can be weightless under special conditions). If you know the mass of something in kilograms and want its weight in newtons, at Earth's surface, you can take advantage of the formula that relates weight and mass. Weight = mass x acceleration due to gravity W = mg This is in accord with Newton's 2nd law, written as F = ma. When the force of gravity is the only force, the acceleration of any object of mass m will be g, the acceleration of free fall. Importantly, g acts as a proportionality constant, 9.8 N/kg, which is equivalent to 9.8 m/s. Sample Question: How much does a 1-kg bag of nails weigh on Earth? W= mg = (1 kg)(9.8 m/s) = 9.8 m/s = 9.8 N. or simply, W= mg = (1 kg)(9.8 N/kg) = 9.8 N. Answer the following questions: Felicia the ballet dancer has a mass of 45.0 kg. 1. What is Felicia's weight in newtons at Earth's surface? From F=ma, we see that the unit of force equals the units [kg x m/s]. Can you see the units [m/s] = [N/kg]? 9.8 m/s 2. Given that 1 kilogram of mass corresponds to 2.2 pounds at Earth's surface, what is Felicia's weight in pounds on Earth? 3. What would be Felicia's mass on the surface of Jupiter? 4. What would be Felicia's weight on Jupiter's surface, where the acceleration due to gravity is 25.0 m/s? Different masses are hung on a spring scale calibrated in newtons. The force exerted by gravity on 1 kg = 9.8 N. 5. The force exerted by gravity on 5 kg = 59.8 N N N. 6. The force exerted by gravity on kg = 98 N. Make up your own mass and show the corresponding weight: The force exerted by gravity on kg = N. By whatever means (spring scales, measuring balances, etc.), find the mass of your physics book. Then complete the table. 1 kg OBJECT MASS WEIGHT MELON APPLE 1 kg 1 N BOOK A FRIEND 60 kg Hewitt Ires wit!