An entomologist would like to confirm that the average honeybee picks up 2000 gr
ID: 1602203 • Letter: A
Question
An entomologist would like to confirm that the average honeybee picks up 2000 grains of pollen every time that it pollenates a flower. He decides to use a magnetic field to do so. a. When bees fly through the air, they acquire an electrical charge because of friction from air resistance. Let q_bee = 83 times 10^-12 C. Let each grain of pollen have an excess of two electrons (q_pollen grain = -3.204 times 10^-19 C). If the bee carries 2000 grains of pollen, what is the total charge of the bee when carrying this pollen? b. The mass of a typical honeybee is 0.175 g. The mass of a typical grain of pollen is 6 times 10^-7 g. If the bee carries 2000 grains of pollen, what is the total mass of the bee when carrying this pollen? c. Using a high speed camera, the entomologist measures speed of the bee's flight to be 6.7 m/s. The pollen carrying bee flies into a region where the magnetic field points into the page, as shown below, and has a strength of 0.5 T. The magnetic force causes the bees to move in a circular path so that F_magnetic = F_centripetal with F_centripetal = m v^2/r where v is the speed of the bee, r is the radius of the circle, and m is the total mass (in kilograms) of the bee with its pollen (m = m_bee + m_pollen). What is the radius of the path for this bee that is carrying her 2000 grains of pollen? d. Based on your answer in part c, do you think this is a reasonable experiment? Or is it unrealistic to try to measure the amount of pollen a bee can carry this way?Explanation / Answer
given
a)
charge of bee is q_b = 83*10^-12 C
charge of pollen q_p = -3.204*10^-19 C
charge of 2000 grains of pollen is q_p*2000 = -3.204*10^-19*2000 C = (-6.408)*10^-16 C
so the total charge of the bee is q_T =q_b+q_p*2000 = 83*10^-12 +(-6.408)*10^-16 C = 8.29993592*10^-11 C = 8.3*10^-11 C
b)
mass of bee is m_b = 0.175 g = 175*10^-6 kg,
mass of each grain of pollen = 6*10^-7 g = 6*10^-10 kg
mass of 2000 grains of pollen is = 6*10^-10*2000 kg = 1.2*10^-6 kg
so total mass of bee with 2000 grains of pollen is = 175*10^-6 +1.2*10^-6 kg = 0.0001762 kg = 0.1762 g
c)
B = 0.5 T
v = 6.7 m/s
F_cen = F_mag
mv^2/r = Bqv sin90
r = mv/Bq
r = (1.2*10^-6*6.7)/(0.5*8.3*10^-11 ) m
r = 193734.94 m
r = 193.73494 km
d)
this is not a reasonable experiment