Chapter 1: Mechanics

A bird is flying due east. Its distance from a tall building is given by

$x\left(t\right)=28.0m+\left(12.4m/s\right)t-\left(0.0450 m/s^3\right)t^3$.What is the instantaneous velocity of the bird when t = 8.00 s?

Question: The coefficient of performance K = H/P is a dimensionless quantity. Its value is independent of the units used for H and P, as long as the same units, such as watts, are used for both quantities. However, it is common practice to express H in Btu/h and P in watts. When these mixed units are used, the ratio H/P is called the energy efficiency ratio (EER). If a room air conditioner has K = 3.0, what is its EER?

A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by

$\overrightarrow{\mathbf{v}}\mathbf{=}\left[5.0m/s-\left(0.0180m/s^3\right)t^2\right]\hat{\mathbf{i}}\mathbf{+}\left(2.0m/s+0.550m/s^{2}t\right)\hat{\mathbf{j}}$.

(a) What are${\mathit{a}}_{\mathbf{x}}\left(t\right)$and${\mathit{a}}_{\mathbf{y}}\left(t\right)$, the x- and y-components of the car’s velocity as functions of time?

(b) What are the magnitude and direction of the car’s velocity at$\mathit{t}\mathbf{=}\mathbf{8}\mathbf{.}\mathbf{0}\mathbf{}\mathit{s}$?

(c) What are the magnitude and direction of the car’s acceleration at$\mathit{t}\mathbf{=}\mathbf{8}\mathbf{.}\mathbf{0}\mathbf{}\mathit{s}$?

A wheel is rotating about an axis that is in the z-direction. The angular velocity${\mathit{\omega }}_{\mathbf{Z}}$ is -6.00 rad/s at t = 0 , increases linearly with time, and is +4.00 rad/s at t = 7.00 s . We have taken counter-clockwise rotation to be positive. (a) Is the angular acceleration during this time interval positive or negative? (b) During what time interval is the speed of the wheel increasing? Decreasing? (c) What is the angular displacement of the wheel at t = 7.00 s ?

In a physics lab, you attach a 0.200-kg air-track glider to the end of an ideal spring of negligible mass and start it oscillating. The elapsed time from when the glider first moves through the equilibrium point to the second time it moves through that point is 2.60 s. Find the spring’s force constant.

Question: Calculate the energy change required for an electron to move between states: a quantum jump up or down an energy-level diagram.

Calculate the moment of inertia of a uniform solid cone about an axis through its center (given figure). The cone has massM and altitudeh .

The radius of its circular base is R .

Knocking Over a Post. One end of a post weighing 400 Nand with height hrests on a rough horizontal surface with${\mathit{\mu }}_{\mathbf{S}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{30}$. The upper end is held by a rope fastened to the surface and making an angle ofwith the post (Given figure). A horizontal forceis exerted on the post as shown.

1. If the forceis applied at the midpoint of the post, what is the largest value it can have without causing the post to slip?
2. How large can the force be without causing the post to slip if its point of application is $\frac{\mathbf{6}}{\mathbf{10}}$of the way from the ground to the top of the post?
3. Show that if the point of application of the force is too high, the post cannot be made to slip, no matter how great the force. Find the critical height for the point of application.

Jonathan and Jane are sitting in a sleigh that is at rest on frictionless ice. Jonathon’s weight is 800 N, Jane’s weight is 600 N, and that of the sleigh is 1000 N. They see a poisonous spider on the floor of the sleigh and immediately jump off. Jonathan jumps to the left with a velocity of 5.00 m/s at 30⁰ above the horizontal (relative to the ice), and Jane jumps to the right at 7.00 m/s at 36.9⁰ above the horizontal (relative to the ice). Calculate the sleigh’s horizontal velocity (magnitude and direction) after they jump out.

You are testing a small flywheel (radius 0.166 m) that will be used to store a small amount of energy. The flywheel is pivoted with low-friction bearings about a horizontal shaft through the flywheel’s center. A thin, light cord is wrapped multiple times around the rim of the flywheel. Your lab has a device that can apply a specified horizontal force $\overrightarrow{F}$ to the free end of the cord. The device records both the magnitude of that force as a function of the horizontal distance the end of the cord has traveled and the time elapsed since the force was first applied. The flywheel is initially at rest. (a) You start with a test run to determine the flywheel’s moment of inertia I. The magnitude F of the force is a constant 25.0 N, and the end of the rope moves 8.35 m in 2.00 s. What is I? (b) In a second test, the flywheel again starts from rest but the free end of the rope travels 6.00 m; Fig. P10.90 shows the force magnitude F as a function of the distance d that the end of the rope has moved. What is the kinetic energy of the flywheel when d = 6.00 m? (c) What is the angular speed of the flywheel, in rev>min, when d = 6.00 m?