Exploring Electric Forces and Hydrogen Bonds in Water Molecules: A Physics Perspective | Assignments Physics

Physics 2130 Discussion 8 worksheet

NAME ________________________________________________________

Learning outcomes:

• Use and manipulate vectors to represent physical quantities like force (net force)

• Describe the conceptual and mathematical models of non-touching forces: electric forces

• Predict attractive and repulsive electric forces (magnitude and direction)

• Predict the motion of interacting (colliding) objects using conservation of momentum, impulse, and Newton’s

laws

• Characterize and make predictions for random motion and diffusion processes using the mean free path length,

the diffusion constant, probability functions, and the rms distance

1. Charged objects can attract neutral matter through the polarization of the neutral

matter – pushing the parts that have the same electric charge slightly further away.

At the molecular level, neutral molecules with separated parts that are positive and

negative can also attract one another by orienting properly. One example of this is

hydrogen bonding of water molecules. This is the primary mechanism that creates

surface tension in water, and a similar phenomenon plays a big role in a variety of biochemistry.

The two hydrogens in a water molecule are positive, each with a charge

+𝑒, and the oxygen is negative, with a charge −2𝑒 (𝑒 =

1.602 ×10−19 𝐶). Electric forces and the quantum sharing of

electrons hold the whole molecule together. Here we will explore how

the electric forces between water molecules can be attractive when

properly arranged. The angle between hydrogen atoms in a water

molecule is actually 104°, but for simplicity we’ll treat them as if they

were a right angle, 90°. A sketch of how the water molecules are aligned in a water-water hydrogen bond is

shown here. In a single water molecule, the distance between the oxygen atom and a hydrogen atom (the

distance between A and B labeled 𝑑) is about 96 𝑝𝑚 (1 𝑝𝑚 = 1 × 10−12 𝑚). The distance between the water

molecules (the distance between B and D labeled 2𝑑) is about twice as far: 192 𝑝𝑚. (Note: 𝑘 =

8.99 ×109 𝑁 ⋅ 𝑚2𝐶2

⁄)

To have a stable bond between the water molecules, the net force on the DEF molecule due to the ABC

molecule must be zero; this means the forces on the DEF molecule must be balanced. We will start by

considering the “backbone” of the hydrogen bond composed of charges A, B, and D.

a. What is the electric force between A and D? What direction is this force on D?

b. What is the electric force between B and D? What direction is this force on D?

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Physics 2130 Discussion 8 worksheet NAME ________________________________________________________ Learning outcomes:

Use and manipulate vectors to represent physical quantities like force (net force)
Describe the conceptual and^ mathematical models of non-touching forces: electric forces
Predict attractive and repulsive electric forces (magnitude and direction)
Predict the motion of interacting (colliding) objects using conservation of momentum, impulse, and Newton’s laws
Characterize and make predictions for random motion and diffusion processes using the mean free path length, the diffusion constant, probability functions, and the rms distance

Charged objects can attract neutral matter through the polarization of the neutral matter – pushing the parts that have the same electric charge slightly further away. At the molecular level, neutral molecules with separated parts that are positive and negative can also attract one another by orienting properly. One example of this is hydrogen bonding of water molecules. This is the primary mechanism that creates surface tension in water, and a similar phenomenon plays a big role in a variety of biochemistry. The two hydrogens in a water molecule are positive, each with a charge +𝑒, and the oxygen is negative, with a charge − 2 𝑒 (𝑒 =
1. 602 × 10 −^19 𝐶). Electric forces and the quantum sharing of electrons hold the whole molecule together. Here we will explore how the electric forces between water molecules can be attractive when properly arranged. The angle between hydrogen atoms in a water molecule is actually 104°, but for simplicity we’ll treat them as if they were a right angle, 90°. A sketch of how the water molecules are aligned in a water-water hydrogen bond is shown here. In a single water molecule, the distance between the oxygen atom and a hydrogen atom (the distance between A and B labeled 𝑑) is about 96 𝑝𝑚 ( 1 𝑝𝑚 = 1 × 10 −^12 𝑚). The distance between the water molecules (the distance between B and D labeled 2 𝑑) is about twice as far: 192 𝑝𝑚. (Note: 𝑘 =
2. 99 × 109 𝑁 ⋅ 𝑚^2 ⁄𝐶^2 ) To have a stable bond between the water molecules, the net force on the DEF molecule due to the ABC molecule must be zero; this means the forces on the DEF molecule must be balanced. We will start by considering the “backbone” of the hydrogen bond composed of charges A, B, and D. a. What is the electric force between A and D? What direction is this force on D? b. What is the electric force between B and D? What direction is this force on D?

c. Are the forces that you calculated in parts a and b balanced? If not, determine the magnitude and direction of the net force. d. Will charge C contribute significantly to the net force on molecule DEF? What sort of force must charges E and F feel from A and B? Explain your reasoning.

A baseball traveling to the left at speed 33 𝑚/𝑠 is hit by a bat moving to the right at speed 25 𝑚/𝑠. Afterward, the ball is returned to the right at speed 36 𝑚/𝑠. The bat continues traveling to the right after hitting the baseball. The masses of the ball and bat are 0. 15 𝑘𝑔 and 0. 94 𝑘𝑔 respectively. a. Draw a before and after picture of this interaction, indicating the velocities of both objects. Is it reasonable to assume that the impulses from any external forces on the bat and baseball are ze ro? Explain your reasoning. b. What is the change in momentum of the baseball? What is the change in momentum of the bat? c. What is the final velocity of the bat?

Listeria, like all bacteria, emit small molecules as waste products or for signaling. Here we will consider a “race” between a Listeria bacterium (about 1 𝜇𝑚 across) and a chemical signal it emits while inside a much larger (∼ 15 𝜇𝑚) mammalian cell. Suppose the Listeria, when at one end of the mammalian cell, emits a pulse of signaling molecules with diffusion constant 𝐷 = 200 𝜇𝑚^2 /𝑠. The Listeria then moves along a straight line from one end of the mammalian cell to the other at a constant speed of about 5 𝜇𝑚/𝑠. a. How long does it take the Listeria to reach the other side of the mammalian cell? b. Assuming the diffusion is two-dimensional, about how long does it take the signaling molecules to reach the other side of the mammalian cell? c. On the graph, sketch two lines: one representing the position of the Listeria as a function of time, and the other representing the rms distance of the signaling molecules as a function of time. (We are interested just in the shape of the graph, so you don’t need to include numerical scales on the axes.) d. Use your results above to decide whether directed motion or diffusion is faster in this scenario. Is there any scenario when they would be reversed? Explain your reasoning. e. About how big would a cell have to be for directed motion to be faster?

Position/𝑟𝑟𝑚𝑠

Exploring Electric Forces and Hydrogen Bonds in Water Molecules: A Physics Perspective, Assignments of Physics

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