A space station is in the shape of a hollow ring, 450 meter in diameter as given in the figure. At how many revolutions per minute should it rotate in order to simulate Earth's gravity-that is, so the normal force on an astronaut at the outer edge would equal the astronaut's weight on Earth?

A child sleds down an 8.5 degree slope at constant speed. What's the frictional coefficient between slope and sled?

Patients with severe leg breaks are often placed in traction, with an external force countering muscles that would pull too hard on the broken bones. In the arrangement shown in given figure, the mass $m$ is $4.8 \mathrm{~kg}$, and the pulleys can be considered massless and frictionless. Find the horizontal traction force applied to the leg.

If initially $m_{\mathrm{A}}$ is at rest $1.250 \mathrm{~m}$ from the edge of the table, how long does it take to reach the edge of the table if the system is allowed to move freely?

The three masses shown in (Figure 1) are connected by massless, rigid rods. Assume that m1 = 100 g and m2 = 300 g. What is the x-coordinate of the center of mass? What is the y-coordinate of the center of mass?

A slender bar of length $l$ and mass $m$ is rigidly attached to the center of a thin circular disk of radius $R$ and mass $m$. The composite object undergoes a motion in which the bar rotates in the horizontal plane with constant angular velocity $\omega_0$ about the center of mass of the composite object and the disk rolls on the floor. Show that $\omega_0=2 \sqrt{g / R}$.

A mass $m_1$ undergoes circular motion of radius $R$ on a horizontal frictionless table, connected by a massless string through a hole in the table to a second mass $m_2$ as shown in figure. If $m_2$ is stationary, find expressions for

(a) the string tension

(b) the period of the circular motion.

A camper hangs a 26-kg pack between two trees using separate ropes of different lengths, as shown in Fig. 5.32. Find the tension in each rope.

A space station is shaped like a ring and rotates to simulate gravity. If the radius of the space station is 120 m, at what frequency must it rotate so that it simulates Earth's gravity? [Hint: The apparent weight of the astronauts must be the same as their weight on Earth.)

A police officer investigating an accident estimates that a moving car hit a stationary car at 25 km/h. Before the collision, the car left 47-m-long skid marks as it braked. The officer determines that the coefficient of kinetic friction was $0.71$. What was the initial speed of the moving car?

The handle of a 22-kg lawnmower makes a $35degree angle with the horizontal. If the coefficient of friction between lawnmower and ground is 0.68, what magnitude of force, applied in the direction of the handle, is required to push the mower at constant velocity? Compare with the mower's weight.

Write a program that prompts the user to enter the number of students, the students’ names, and their scores, and prints student names in decreasing order of their scores.

Write a program that asks the user to enter the month (letting the user enter an integer in the range of 1 through 12) and the year. The program should then display the number of days in that month. Use the following criteria to identify leap years: 1. Determine whether the year is divisible by 100. If it is, then it is a leap year if and only if it is divisible by 400. For example, 2000 is a leap year but 2100 is not. 2. If the year is not divisible by 100, then it is a leap year if and if only it is divisible by 4. For example, 2008 is a leap year but 2009 is not. Here is a sample run of the program: Enter a month (1-12): 2 [Enter] Enter a year: 2008 [Enter] 29 days

You're in traffic court, arguing against a speeding citation. You entered a 210 -m-radius banked turn designed for 80 km/h, which was also the posted speed limit. The road was icy, yet you stayed in your lane, so you argue that you must have been going at the design speed. But police measurements show there was a frictional coefficient $\mu=0.15$ between tires and road. Is it possible you were speeding, and if so by how much?