2003 FALL QUIZ 10

1. A bottle has a mass of 35.00g when empty and 98.44g when filled with water. When filled with alcohol, whose specific gravity is 0.79, what is the total mass of the bottle?

Solution

We find the mass of the water from

             m_water = 98.44g - 35.00g = 63.44g.

We find the volume of the water from

           V_water  = m_water /r_water  = 63.44g/(1g/cm³) = 63.44cm³ = V_alcohol.

We find the mass of the alcohol from 

            m_alcohol = r_alcoholV_alcohol = SG_alcoholr_waterV_alcohol = (0.79)(1g/cm³)(63.44cm³)

                         = 50.12g

Therefore the total mass of the bottle is

            m = m_bottle+ m_alcohol = 35.00g + 50.12g = 85.12g.

2. A 1500-kg elephant stands on its four feet. Each foot has an area of 800cm². What is the pressure the elephant exerts on the ground?

Solution

We find the pressure from

             P = F/A = mg/A = (1500kg)(9.80m/s²)/4(800 x 10^-4m²) = 4.6 x 10⁴N/m².