PROBLEMAS PROPUESTOS 1. Tres bloques con pesos de \( 1 \mathrm{kp}, 2 \mathrm{kp} \) y \( 3 \mathrm{kp} \) están apilados sobre una mesa, el menor arriba y el mayor está abajo. Haga un diagrama y analice este sistema en términos de los pares de fuerzas de la tercera ley de newton. 2. Tres fuerzas actúan sobre un cuerpo que se mueve en una línea recta con una rapidez constante. Si dos de las fuerzas son: \( F_{1}=(4.5 \mathrm{~N},-1.5 \mathrm{~N}) \) y \( \mathrm{F}_{2}=(-3.5 \mathrm{~N},-1 \mathrm{~N}) \), ¿Cuál es la tercera fuerza? Resp: \( F_{3}=(-1 \mathrm{~N}, 2.5 \mathrm{~N}) \) 3. Hallar la lectura del dinamómetro. Resp: \( 10 \mathrm{~N} \) 4. Construir los diagramas de cuerpo libre (D. C. L.) de las figuras a), b) y c) mostradas: 5. Calcule las tensiones \( T_{1} \) y \( T_{2} \) en las figuras siguientes: Resp: a) \( \mathrm{T}_{1}=\mathbf{2 . 3 1} \mathrm{kp}, \mathrm{T}_{2}=\mathbf{4 . 6 2} \mathrm{kp} \) b) \( T_{1}=34.64 \mathrm{~N}, \quad \mathrm{~T}_{2}=20 \mathrm{~N} \) Figura (a) Figura (b) 6. Hallar los módulos de las fuerzas A y B para equilibrar al cuerpo mostrado en la figura: Resp: \( A=79.9 \mathrm{~N} ; B=60.2 \mathrm{~N} \) 7. Un cilindro pesa \( 3.15 \mathrm{kp} \). Calcular la tensión en el cable y la reacción en la pared, si la superficie de contacto es lisa. Ver figura. Resp: \( T=3.39 \mathrm{kp} ; \quad R=1.26 \mathrm{kp} \) 8. En la figura mostrada, de terminar la tensión en la cuerda y la reacción en la pared, sabiendo que el peso de la barra es despreciable. Resp: \( \mathbf{T}=626.1 \mathrm{kp} ; \mathbf{R}=376.8 \mathrm{kp} \) 9. En el sistema en equilibrio mostrado en la figura, hallar la fuerza de compresión y la tensión de la barra, el peso de la barra es despreciable y lleva un peso en un extremo, \( w=40 \mathrm{kp} \) Resp: \( T=69.3 \mathrm{kp} ; \mathrm{F}=80 \mathrm{kp} \) 10. En el sistema mostrado en la figura, hallar la fuerza de compresión y la tensión de la barra, se desprecia el peso de la barra. \( (w=50 \mathrm{kp}) \) Resp: \( \mathbf{T}=\mathbf{5 0} \mathrm{kp} ; \mathbf{R}=\mathbf{5 0} \mathbf{~ k p} \)
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According to Newton's third law, for every action, there is an equal and opposite reaction. In this case, the force exerted by the 3 kp block on the 2 kp block is equal and opposite to the force exerted by the 2 kp block on the 3 kp block. Similarly, the force Show more…
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Pan B: Moving in a horizontal circle Calculate given the masses of the swinging and hanging objects. Combine this with the results from the third video. Does it seem reasonable? Theory: This is a side view of the Experiment, showing the forces acting on the hanging mass in equilibrium. The third video includes 40 revolutions of the swinging mass for three different values of L: 0.75, 1.0, and 1.25. Note that these three values are referred to as "radius" in the video but strictly speaking, they are the length of the string. But since we have the angle θ, we might as well do a bit of trigonometry and calculate the actual radius. Mass of swinging mass and mass of hanging mass, length of string from top of tube to swinging mass. Calculate the following table using the third video as the time for 40 revolutions: Period (T) Radius (r) Speed (v) Tension Weight Plotting the Data Use whatever software you choose to plot speed squared (v²) vs radius (r) and find the best-fit line to the data. Paste the graph below (it should include the individual data points and the best-fit line) and write down the equation for your best-fit line. Write down Newton's Second Law for the swinging mass in the radial and vertical directions, including the expression for centripetal acceleration. Radial direction: Vertical direction: By using the equations above, find the relationship between speed and radius. You should find that v² is proportional to r, that is v² = Cr, where C is a proportionality constant. Using the fact that the tension equals the weight of the hanging mass, write C in terms of the masses and gravitational acceleration g. Comparing Data and Theory Compare the value of the slope for the line above to the value for the slope given by the formula for the proportionality constant. Calculate the percent relative error. Data and Calculation: Note that for any value of L, θ is the same since sin θ = m/M.
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A parallel-plate capacitor with plates of area 25.0 cm² and 2.00 mm separation is charged to a potential difference of 250 V and disconnected from the source. The capacitor is then immersed in distilled water. Assuming the liquid is an insulator, determine (a) the capacitance before and after immersion, (b) the potential difference after immersion, and (c) the change in energy of the capacitor.
For Problems $7-18$, please do the following. (a) Draw a scatter diagram displaying the data. (b) Verify the given sums $\Sigma x, \Sigma y, \Sigma x^{2}, \Sigma y^{2}$, and $\sum x y$ and the value of the sample correlation coefficient $r$. (c) Find $\bar{x}, \bar{y}, a$, and $b$. Then find the equation of the least-squares line $\hat{y}=a+b x$ (d) Graph the least-squares line on your scatter diagram. Be sure to use the point $(\bar{x}, \bar{y})$ as one of the points on the line. (e) Interpretation Find the value of the coefficient of determination $r^{2}$. What percentage of the variation in $y$ can be explained by the corresponding variation in $x$ and the least-squares line? What percentage is unexplained? Answers may vary slightly due to rounding. Archaeology: Artifacts Data for this problem are based on information taken from Prehistoric New Mexico: Background for Survey (by D. E. Stuart and R. P. Gauthier, University of New Mexico Press). It is thought that prehistoric Indians did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let $x$ be the elevation (in thousands of feet) of an archaeological site in the southwestern United States. Let $y$ be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. The following data were obtained for a collection of archaeological sites in New Mexico: $$ \begin{array}{l|ccccc} \hline x & 5.25 & 5.75 & 6.25 & 6.75 & 7.25 \\ \hline y & 19 & 13 & 33 & 37 & 62 \\ \hline \end{array} $$ $$ \begin{aligned} &\text { Complete parts (a) through (e), given } \Sigma x=31.25, \Sigma y=164, \Sigma x^{2}=197.813 \text { , }\\ &\Sigma y^{2}=6832, \Sigma x y=1080, \text { and } r \approx 0.913 . \end{aligned} $$ (f) At an archaeological site with elevation $6.5$ (thousand feet), what does the least-squares equation forecast for $y=$ percentage of culturally unidentified artifacts?
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