Classical Mechanics
# Mechanics Warmups

**in km/hr**?

The average human heart pumps \(5~\mbox{L/min}\) of blood through the human body at a pressure of \(10^4~\mbox{Pa}\). For a person who lives 80 years, what is the total energy output of his heart **in Joules**?

**Details and assumptions**

- Assume that the cardiac output is constant for any age.
- There are 365.25 days in one year, and 24 hours in a day.

If Josh wants the coffee to be as hot as possible when he gets back to the lab, at what point should he add the creamer to the coffee?

Its popularity is due in part to the ease with which it can be modified to shoot faster and farther. One easy modification is to insert a secondary spring inside the main spring, as shown below:

If the strength (spring constant) of the first spring is \(k\), and the strength of the second spring is \(\frac12 k\), what is the strength of the two springs together?

Consider a system of \(N\) particles whose coordinates are \(\mathbf{r}_i = \{r_i^x,r_i^y,r_i^z\}\), and whose velocities are \(\dot{\mathbf{r}}_i\).

Each pair of particles \(\left(i, j\right)\) interacts through a potential \(V\left(\mathbf{r}_i, \mathbf{r}_j\right)\) which depends on the coordinates \(\left(\mathbf{r}_i, \mathbf{r}_j\right)\) only through their difference, i.e. \[V\left(\mathbf{r}_i, \mathbf{r}_j, t\right) = V\left(\mathbf{r}_i-\mathbf{r}_j, t\right)\] As the system evolves in time, which of the following bulk quantities must be conserved?

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