18. Soccer is also called “association football.\" A soccer ball is a sphere, wi

Question

18. Soccer is also called “association football." A soccer ball is a sphere, with a circumference of 70 centimeters [cm]. In developing a new material to use for a soccer ball when NASA attempts to colonize Mars, you test a material with a specific gravity of 1.21. Assume the ball will be a solid sphere made from this material. What is the weight in units of newtons [N] of the ball on Mars? Recall gravity on Mars is 3.7 meters per second squared [m/s] Recall the circumference of a circle is equal to the diameter times pi: C = D 7. The European Space Agency launched a probe called Rosetta in March 2004. In August 2014 Rosetta reached its destination: a comet called 67P/Churyumov-Gerasimenko. Rosetta is the first spacecraft to rendezvous with a comet It contained a lander craft, called Philac The Rosetta has a launch mass on Earth of 3000 kilograms [kg] and the Philae has a launch mass of 220 pound-mass [lb ]. In order to escape Earth's gravity, the combined space craft [mi/h How much thrust, in t must accelerate at a rate of 25,000 miles per hour squared units of newtons [NJ. must the engines provide to reach this acceleration?

Explanation / Answer

18. density of the ball material = specific gravity * 1000 kg/m^3
                                 = 1.21 * 1000 kg/m^3
                                 = 1210 kg/m^3

    Circumference = 70 cm
    3.14 * D = 70

    D = 70/3.14 cm = 22.29 cm

    r = D/2 = 22.29/2 = 11.14 cm

    Volume of the ball = 4/3 * 3.14 * r^3
                       = 4/3 * 3.14 * (0.1114)^3
                       = 0.005788 m^3

    Total mass of the ball = 1210 * 0.005788 = 7.003 Kg
    Weight of the ball = 7.003 * 3.7 = 25.912 N

7. 1 lb = 0.453592 Kg
   220 lb = 220 * 0.453592 Kg
          = 99.7 kg

    Mass of philae = 99.7 kg
    Mass of Rosetta = 3000 kg
    Total mass = 3099.7 kg

    accleraration = 25000 * 1609.34/(3600 * 3600) = 3.104 m/sec^2

    Thrust needed by the rocket = mass * accleartion
                                = 3099.7 * 3.104
                                = 9621.4 N

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