Mathematical Homework Assignment
For all your answers, write down your calculations and explain your reasoning. Draw sketches whenever helpful, and use your units correctly. If you are using any online resources (such as unit conversion tools) give their URL and webpage title in your answers.
[a] A liter is a measure of volume equal to 1000 cc (cm). About how tall do you think a person with a body volume (head + limbs + torso) of Z liters would be? Feel free to make measurements of your own body to get useful data that would help you answer this question.
[b] Let’s say this person also happens to have a mass of Z kilograms (kg). How many pounds would this person weigh?
[c] What would be the density of this person? Give the answer in units of kg ni3 and in g/cc.
[d] Does this density seem reasonable to you? In other words, do you think a person could be about that tall and weigh about that much? Why or why not?
For all your answers, write down your calculations and explain your reasoning. Draw sketches whenever helpful, and use your units correctly. If you are using any online resources (such as unit conversion tools) give their URL and webpage title in your answers.
[a] In the equation E = mc’ discovered by Albert Einstein in 1905, c is the speed of any particle of light traveling through vacuum. It is defined to be exactly 299,792,458 meters per second (m s’). What, then is c’ and what units should that quantity have? flow many digits are significant in that answer? Explain why.
[b] An object with a mass of Y kilograms would be equal in mass to about how many paper clips? As always, explain your reasoning and show all calculations that you use.
[c] If that object’s mass were converted into energy, how much energy would result? Make sure to give your answers in units of kilogram meters squared per second squared (kg m2 s’). Two digits of your answer are significant.
[d] Does that amount of energy seem like a lot or a little? Explain your answer, citing any sources you use.
For all your answers, write down your calculations and explain your reasoning. Draw sketches whenever helpful, and use your units correctly. If you are using any online resources (such as unit conversion tools) give their URL and webpage title in your answers.
[a] You are about to lift a small child off the ground. This child weighs Z pounds. How many newtons of gravitational force downward does this child produce?
[b] Use a ruler to measure, to the nearest centimeter, the distance from: The center of your hand to your elbow. Let’s call this distance r,. Your elbow to your shoulder. Let’s call this distance r2. Your shoulder to your lower back (spine). Let’s call this distance r3.
[c] If you lift the child up off the ground, you will experience a moment of force — that is, a torque — on the set of joints from your hand to your spine. Draw a simple sketch (a stick figure is fine) of the physical system where you lift the child with your outstretched arms bent over at your waist, and compute the torque (in units of newton meters, or N m) at your elbow (distance r,), at your shoulder (r, + r2), and at your spine (r, + r2+ r3).
[d] A set of small muscles are attached to your spine at a distance of about 2 inches (0.05 m) from the spine itself. Those muscles must exert force to balance the torque you experience when lifting the child. How much force will those back muscles experience? How many times more force is that than the actual weight of the child?
[e] If, rather than bending at the waist with outstretched arms, you instead stand close to the child, bend at the knees, and lift by straightening your legs while keeping your back close to vertical, how much force will those back muscles experience? Draw a sketch of this physical system to show where the torques would be. What do you think would be the health advantages or disadvantages of this lifting method?
3. Watch Segment D (Vectors and Scalars), Segment E (Graphical Resolution of Vectors) and Segment F (Mathematic Resolution of Vectors) at https://www.gpb.org/physics-in-motion (The GPB Physics In Motion video series). Then write answers to the following questions, showing all your calculations.
[a] A child with mass Y kilograms (kg) who is skating eastward in a hockey rink at Y centimeters per second (cm/s) runs into another child, also with mass Y kg, who is skating northward at Z cm/s. The children grab onto each other and keep moving across the ice. Draw a diagram of this interaction, labeling all the relevant objects, quantities, and velocity vectors before and after the collision.
[b] What is the velocity (magnitude and direction) of the two children after they collide? Your answer should be significant to two digits.
[c] Do you think these two children are likely to have been injured in the collision? In a paragraph of at most 50 words, explain using scientific and mathematical reasoning why you think so or not. List any reference sources, such as books or websites, if you used them to help you come to your conclusion.
