Suppose you attempt to pick up a very heavy object. Before you tried to pick it up, the object was sitting still—its momentum was not changing. You pull very hard, but do not succeed in moving the object. Is this a violation of the Momentum Principle? How can you be exerting a large force on the object without causing a change in its momentum? What does change when you apply this force?

a. Naming What types of graphs can you use to analyze the acceleration of an object? b. Describing Describe the motion of an object if its speed-versus-time graph is a horizontal line. c. Predicting What would a distance-versustime graph look like for the moving object in part (b)?

Photodissociation of water

$$\mathrm{H}_2 \mathrm{O}(l)+h v \longrightarrow \mathrm{H}_2(g)+\frac{1}{2} \mathrm{O}_2(g)$$

has been suggested as a source of hydrogen. The energy for the reaction is $285.8 \mathrm{~kJ}$ per mole of water decomposed. Calculate the maximum wavelength (in $\mathrm{nm}$ ) that would provide the necessary energy. In principle, is it feasible to use sunlight as a source of energy for this process?

Why is the following situation impossible? An air rifle is used to shoot 1.00-g particles at a speed of vx = 100 m/s. The rifle’s barrel has a diameter of 2.00 mm. The rifle is mounted on a perfectly rigid support so that it is fired in exactly the same way each time. Because of the uncertainty principle, however, after many firings, the diameter of the spray of pellets on a paper target is 1.00 cm.

Will help you prepare for the material covered in the first section of the next chapter. Solve each equation by using rhe cross-products principle to clear fractions from the proportion:

$$\text { If } \frac { a } { b } = \frac { c } { d } , \text { then } a d = b c . ( b \neq 0 \text { and } d \neq 0 )$$

Round to the nearest tenth. Solve for

$$B , 0 < B < 180 ^ { \circ } : \frac { 81 } { \sin 43 ^ { \circ } } = \frac { 62 } { \sin B }$$

use Archimedes’ Principle, which states that when a sphere of radius r with density

$$d_s$$

is placed in a liquid of density

$$d_L=62.5lb/ft^3$$

,it will sink to a depth h where .

$$\dfrac{π}{3}(3rh^2-h^3)d_L=\dfrac{4}{3}πr^3d_s$$

Find an approximate value for h if:

$$r=5 ft$$

and

$$d_s=20lb/ft^3$$

A rocket sled with a mass of 2900 kg moves at 250 m/s on a set of rails. At a certain point, a scoop on the sled dips into a trough of water located between the tracks and scoops water into an empty tank on the sled. By applying the principle of conservation of linear momentum, determine the speed of the sled after 920 kg of water has been scooped up. Ignore any retarding force on the scoop.

Use the uncertainty principle to estimate the binding energy of the $\mathrm{H}_2$ molecule by calculating the difference in kinetic energy of the electrons between when they are in separate atoms and when they are in the molecule. Take $\Delta x$ for the electrons in the separated atoms to be the radius of the first Bohr orbit, $0.053 \mathrm{~nm}$, and for the molecule take $\Delta x$ to be the separation of the nuclei, $0.074 \mathrm{~nm}$. [Hint: Let $\left.\Delta p \approx \Delta p_x.\right]$

Liquid benzene burns in the atmosphere. If a cold object is placed directly over the benzene, water will condense on the object and a deposit of soot (carbon) will also form on the object. The chemical equation for this reaction is of the form x₁C₆H₆ + x₂O₂ → x₃C + x₄H₂O. Determine values of x₁, x₂, x₃, and x₄ to balance the equation.

In a population of rabbits, f (C$_{1}$) = $0.70$ and f (C$_{2}$) = $0.30$. The alleles exhibit an incomplete dominance relationship in which C$_{1}$C$_{1}$ produces black rabbits, C$_{1}$C$_{2}$ tan-colored rabbits, and C$_{2}$C$_{2}$ rabbits with white fur. If the assumptions of the Hardy-Weinberg principle apply to the rabbit population, what are the expected frequencies of black, tan, and white rabbits?

Underline the gerund in the following sentences. Then, identify the function of the gerund by writing above it one of these abbreviations :S for subject, PN for predicate nominative, $D O$ for direct object, 10 for indirect object, or $O P$ for object of a preposition.

The baby sitter talked to the children about the importance of sharing.

An Atwood’s machine that has a frictionless massless pulley and massless strings has a 2.00-kg object hanging from one side and 4.00-kg object hanging from the other side.

$(a)$ What is the speed of each object 1.50 s after they are simultaneously released from rest?

A lens with a power of +10 D is used as a simple microscope. (a) For the image of an object to be seen clearly, can the object be placed infinitely close to the lens, or is there a limit on how close it can be? Explain. (b) Calculate how close an object can be brought to the lens. (c) What is the angular magnification at this point?

Suppose $f$ is differentiable at points on a closed path $\gamma$ and at all points in the region G enclosed by $\gamma,$ except possibly at a finite number of poles of $f$ in G. Let Z be the number of zeros of $f$ in G, and P the number of poles of $f$ in G, with each zero and pole counted as many times as its multiplicity. Show that $\frac{1}{2 \pi i} \oint_{\gamma} \frac{f^{\prime}(z)}{f(z)} d z=Z-P.$ This formula is known as the argument principle.