Suppose that 1000 pollen grains slam into the abdomen of a 5.0 g bee that is hovering just above the flower. the grain's mass is 1.0×10−7g. if the collision is inelastic, what is the bee's speed immediately afterward?

m1 = 5g = 0.005kg v1 = 0 m2 = 1.0 x 10^-7g = 1.0x10^-10kg v2 = 7.5 v3 = ? looks like you did the formula correctly m1v1 + m2v2 = (m1+m2)v3 0 + m2v2 = (m1+m2)v3 m2v2 / (m1+m2) = v3 (1.0x10^-10)(7.5) / (0.005 + 1.0x10^-10) = v3 1.5x10^-7 = v3 However, it said the bee gets hit by 1000 pollen grains, so I would guess you have to multiply 1.0 x 10^-10 by 1000 first, unless the total mass of the 1000 grains really is 1.0 x 10^-10.

johanrusli johanrusli · Answer 2 · 2019-12-18T10:30:50+01:00

The bee's speed immediately afterward is about 1.5 × 10⁻⁴ m/s

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Further explanation

Newton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.

[tex]\large {\boxed {F = ma }[/tex]

F = Force ( Newton )

m = Object's Mass ( kg )

a = Acceleration ( m )

Let us now tackle the problem !

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Complete Question:

Suppose that 1000 pollen grains slam with speed of 7.5 m/s into the abdomen of a 5.0 g bee that is hovering just above the flower. The grain's mass is 1.0×10⁻⁷ g. If the collision is inelastic, what is the bee's speed immediately afterward?

Given:

mass of pollen grains = m₁ = 1.0 × 10⁻⁷ g

number of pollen grains = N = 1000

mass of bee = m₂ = 5.0 g

initial speed of pollen grains = u₁ = 7.5 m/s

initial speed of bee = u₂ = 0 m/s

Asked:

final speed of bee = v = ?

Solution:

We will use law of conservation of momentum to solve this problem as follows:

[tex]Nm_1u_1 + m_2u_2 = Nm_1v_1 + m_2v_2[/tex]

[tex]Nm_1u_1 + m_2u_2 = Nm_1v + m_2v[/tex]

[tex]Nm_1u_1 + m_2u_2 = (Nm_1+m_2)v[/tex] → inelastic v₁ = v₂

[tex]1000(1.0 \times 10^{-7})(7.5) + 5.0(0) = (1000(1.0 \times 10^{-7}) + 5.0)v[/tex]

[tex]7.5 \times 10^{-4} + 0 = 5.0001v[/tex]

[tex]v = 7.5 \times 10^{-4} \div 5.0001[/tex]

[tex]v \approx 1.5 \times 10^{-4} \texttt{ m/s}[/tex]

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Answer details

Grade: High School

Subject: Physics

Chapter: Dynamics