Tutor profile: Ayo C.
Subject: Physics (Electricity and Magnetism)
When two small spheres of equal charge Q are placed 6 cm apart, each one exerts a force F = 40 N on the other. What is Q?
When two charges are near each other, they exert equal and opposite forces on one another. The value of this force is given by Coulomb's Law, which states: F = (k*Q1*Q2)/r^2 where k is the Coulomb's law constant equal to 9.0 x 10^9 N*m^2/C^2, Q1 and Q2 are the charges, and r is the linear distance between them. In this problem we are told that the charges are equal, so we can rewrite coulomb's law to: F = (k*Q^2)/r^2 We are given F and r and we know k, so we can rearrange the equation to solve for Q. F*r^2 = k*Q^2 Q^2 = (F*r^2)/k Q = sqrt[(F*r^2)/k] Before we input our values, we must remember to check our units. The units of the Coulomb's law constant include meters, but r is given to us in centimeters. We convert r to meters by dividing it by 100, since there are 100 centimeters in 1 meter. Q = sqrt[ (40 N * (0.06 m)^2)/ 9.0 x 10^9 N*m^2/C^2 ] Answer: Q = 4.0 x 10^(-6) C or 4.0 µC
What is the limiting reactant for the following reaction given we have 3.4 moles of Ca(NO3)2 and 2.4 moles of Li3PO4? Reaction: 2Ca(NO3)2 + 2Li3PO4 --> 6LiNO3 + Ca3(PO4)2
Think of stoichiometry as a similar process to measuring out recipes. Suppose I have a recipe that calls for 2 cups of flour and 4 eggs in order to make 12 chocolate chip cookies. In my cabinet I have 4 cups of flour and in my refrigerator I have 4 eggs. Even though I have enough flour to theoretically make two batches of cookies, I am limited by the fact that I only have enough eggs for one batch. The eggs are the "limiting reactant". In the reaction above, we can pick a product and see how much of it we can *theoretically* make with each of our reactant amounts. First, let's look at how much product we can make with the Ca(NO3)2: For every 6 moles of LiNO3, I need 2 moles of Ca(NO3)2. Using dimensional analysis, I can take the 2.4 moles of Ca(NO3)2 that I have and multiply it by 6/2. This results in a theoretical yield of 7.2 moles of LiNO3. Next, let's look at Li3PO4: For every 6 moles of LiNO3, I need 2 moles of Li3PO4. Using dimensional analysis, I can take the 3.4 moles of Li3PO4 that I have and multiply it by 6/2. This results in a theoretical yield of 10.2 moles of LiNO3. The limiting reactant is the Ca(NO3)2 since I only have enough of it to make 7.2 moles of LiNO3. This is despite the fact that I have enough Li3PO4 to make 10.2 moles of LiNO3. Note: You would get the same answer if you looked at the theoretical yields of Ca3(PO4)2 instead of LiNO3.
A 30 kg kid swings back and forth in a swing and reaches a maximum height of 1.9 meters above the ground as he is swinging. When no one is in the swing, the seat of the swing hangs 40 cm above the ground. What is the total energy of the kid in the swing?
This is a conservation of energy problem. The total mechanic energy of the system (meaning the child and the swing) always remains the same and it is defined as the sum of the kinetic energy and potential energy at any point in time (TE = GPE + KE). The equation for gravitational potential energy is GPE = m*g*h, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above the ground. The equation for kinetic energy is KE = (1/2)*m*v^(2), where m is the mass of the object and v is the velocity of the object. It follows from these equations that gravitational potential energy is maximized when the child is at the maximum height above the ground. We also know that based on how swings work, the child momentarily stops when they reach this maximum height before swinging in the opposite direction. Therefore, their kinetic energy at this point is zero. So: TE = GPE + KE TE = mgh + 0 TE = mgh The total energy of the kid in the swing is simple equal to the gravitational potential energy when the swing is at its maximum height. TE = (30 kg)*(9.81 m/s^2)*(1.9 m) Answer: TE = 559 J
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