1. Your free body diagram for Part 2 should have looked like this: Construct the free-body diagram. 1. Place the tail of the vectors within the confines of the mass. 2. Orient the vectors by dragging the heads in the proper direction. Note: the angles may be within +15°, the magnitudes are not considered, and the vectors do not need to be centered on the mass. N:90° 1444 FL: 180; 179.87 mg; 270 FR: 0.04⁰ Suppose two children push horizontally, but in exactly opposite directions, on a third child in a wagon. The first child exerts a force F₁ of 65.0 N, the second a force FR of 96.0 N, friction f is 13.0 N, and the mass of the third child plus wagon is 26.0 kg.

A barge is pulled by the two tugboats shown in the following figure. One tugboat pulls on the barge with a force of magnitude 4000 units of force at 15 above the line AB (see the figure and the other tugboat pulls on the barge with a force of magnitude 5000 units of force at 12 below the line AB. Resolve the pulling forces to their scalar components and find the components of the resultant force pulling on the barge. What is the magnitude of the resultant pull? What is its direction relative to the line AB?

Elisha Graves Otis invented the elevator brake in the mid-1800s, making it possible to build tall skyscrapers with fast elevators. Todays skyscrapers are a large fraction of a mile tall; for example. Taipei 101 in Taiwan has 101 stories and is 515 m (0.32 miles) tall. The top speed of the elevator in the Taipei 101 tower is roughly three times greater than the ascent rate of a commercial jet airplane. The position and time data in the table are based on such an elevator. a. Working in SI units, make a position-versus-time graph for the elevator. (You may wish to use a spreadsheet program.) b. Describe the motion of the elevator in words. c. Find the highest speed of the elevator. When is the elevator going at this speed? d. What sort of considerations would the engineers need to make to ensure the comfort of the passengers?

Review. The graph in Figure P7.20 specifies a functional relationship between the two variables u and v. (a) Find abudv. (b) Find baudv. (c) Find abvdu. Figure P7.20

A paper in the journal Current Biology tells of some jellyfish-like animals that attack their prey by launching stinging cells in one of the animal kingdoms fastest movements. High-speed photography showed the cells were accelerated from rest for 700. ns at 5.30 107 m/s2. Calculate (a) the maximum speed reached by the cells and (b) the distance traveled during the acceleration.

A hare and a tortoise compete in a race over a straight course 1.00 km long. The tortoise crawls at a speed of 0.200 m/s toward the finish line. The hare runs at a speed of 8.00 m/s toward the finish line for 0.800 km and then stops to tease the slow-moving tortoise as the tortoise eventually passes by. The hare waits for a while after the tortoise passes and then runs toward the finish line again at 8.00 m/s. Both the hare and the tortoise cross the finish line at the exact same instant. Assume both animals, when moving, move steadily at their respective speeds. (a) How far is the tortoise from the finish line when the hare resumes the race? (b) For how long in time was the hare stationary?

A student at the top of a building of height h throws one ball upward with a speed of i and then throws a second ball downward with the same initial speed i. Just before it reaches the ground, is the final speed of the ball thrown upward (a) larger, (b) smaller, or (c) the same in magnitude, compared with the final speed of the ball thrown downward?

Use the component method to add the vectors A and B shown in Figure P3.9. Both vectors have magnitudes of 3.00 m and vector A makes an angle of = 30.0 with the x axis. Express the resultant A+B in unit-vector notation.

Tectonic plates are large segments of the Earth's crust that move slowly. Suppose that one such plate has an average speed of 4.0 cm/year. (a) What distance does it move in 1 s at this speed? (b) What is its speed in kilometers per million years?

A basin surrounding a drain has the shape of a circular cone opening upward, having everywhere an angle of 35.0 with the horizontal. A 25.0-g ice cube is set sliding around the cone without friction in a horizontal circle of radius R. (a) Find the speed the ice cube must have as a function of R. (b) Is any piece of data unnecessary for the solution? Suppose R is made two times larger. (c) Will the required speed increase, decrease, or stay constant? If it changes, by what factor? (d) Will the time interval required for each revolution increase, decrease, or stay constant? If it changes, by what factor? (e) Do the answers to parts (c) and (d) seem contradictory ? Explain.