1.Several people are riding in a hot-air balloon. The combined mass of the peopl

Question

1.Several people are riding in a hot-air balloon. The combined mass of the people and balloon is 310 kg. The balloon is motionless in the air, because the downward-acting weight of the people and balloon is balanced by an upward-acting “buoyant” force. If the buoyant force remains constant, how much mass should be dropped overboard so that the balloon acquires an upward acceleration of 0.15 m/s2?




2.At the local grocery store, you push a 14.5 kg shopping cart. You stop for a moment to add a bag of dog food to your cart. With a force of 10.6 N, you now accelerate the cart from rest through a distance of 2.29 m in 3.00 seconds. What is the mass of the dog food?

Explanation / Answer

             1.       Given that the mass of people and balloon is m = 310 kg
___________________________________________________       When the weight of the balloon and people balanced by the
      upward buoyant force (F),so
                          F = mg
                              = (310 kg)(9.8 m/s2)
                             = 3038 N
      If the balloon moving with accelerat a = 0.15 m/s2 upwards
                       F - Mg = Ma
                      F = Mg + Ma
                      F = M(g + a)
                     M = F / (g + a)
                         = 3038 N / (9.8 m/s2 + 0.15 m/s2)
                         = 305.326 kg
      Then the removed mass to accelerate the balloon is
             M - m = 310 kg - 305.326 kg
                        = 4.67 kg _________________________________________________________ _________________________________________________________    2.       The mass of the shopping cart, m = 14.5 kg       The force, F = 10.6 N       The distance, y = 2.29 m       Time, t = 3.00 s       The initial velocity of the v0 = 0m/s ___________________________________________________________              Using kinematic relation, we have                                y = v0t + (1/2)at2                    (2.29 m) = 0 + (1/2)a(3.00 s)2       Therefore, the acceleration, a = 0.5089 m/s2       Using the Newton's second law of motion,              Force F = ma                        m = F/a                            = (10.6 N)/(0.5089 m/s2)                            = 20.829 kg       Using the Newton's second law of motion,              Force F = ma                        m = F/a                            = (10.6 N)/(0.5089 m/s2)                            = 20.829 kg ___________________________________________________________       Total mass is given by                   m = 14.5 kg + mass of the dog food(M)       Hence, the mass of the dog food is                          M = m - 14.5 kg                               = 20.829 kg - 14.5 kg                               = 6.329 kg      

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