Concept explainers
The magnitude of the acceleration of the block resting on an inclined plane.

Answer to Problem 80QAP
The magnitude of the acceleration of the block resting on an inclined plane is 3.77 m/s2.
Explanation of Solution
Given info:
Mass of the block placed on the incline
Mass of the hanging block
Angle made by the plane with horizontal
Coefficient of static friction
Coefficient of kinetic friction
Formula used:
Free body diagrams are drawn for the two blocks and the acceleration of the block is determined using the force equations for both the blocks.
The free body diagram for the block of mass
Since m2 is greater than m1, the hanging block would tend to move down and the block on the incline would slide upwards along the incline.
The weight of the block is
The total force acting along the +x direction is given by,
Here, ax is the block s acceleration along the downward direction (+x ).
Draw the free body diagram for the block of mass
The weight
Resolve the weight
Both the blocks have the same magnitude of acceleration.
The force equation along the +x direction is given by,
The force equation along the +y direction is given by,
Since the block is in equilibrium in the y direction,
Hence,
The force of friction and the normal force are related as follows:
The value of the coefficient of friction
Calculation:
First determine, if the system is at rest or in motion.
The system will be at rest if
If the system is at rest, equation (1) can be written as,
Since
Substitute the values of the variables in the above equation,
Calculate the value of
The component
If the system is at rest, assume the maximum force of static friction to act on the block.
Then,
From equation (4),
The component
Calculate the maximum force of static friction acting on the block.
Therefore,
Since it is seen that
Add equations (1)
Substitute the expressions for w2,w1x and fk in the expression and write an expression for ax.
Substitute the values of the variables in the expression and determine the magnitude of the acceleration of the block on the incline.
Conclusion:
The magnitude of the acceleration of the block resting on an inclined plane is 3.77 m/s2.
Want to see more full solutions like this?
Chapter 5 Solutions
COLLEGE PHYSICS,VOLUME 1
- How much is the circumference of a circle whose diameter is 7 feet?C =π darrow_forwardHow to solve 2542/64.132arrow_forwardAssume that you fancy polynomial splines, while you actually need ƒ(t) = e²/3 – 1 for t€ [−1, 1]. See the figure for a plot of f(t). Your goal is to approximate f(t) with an inter- polating polynomial spline of degree d that is given as sa(t) = • Σk=0 Pd,k bd,k(t) so that sd(tk) = = Pd,k for tk = −1 + 2 (given d > 0) with basis functions bd,k(t) = Σi±0 Cd,k,i = • The special case of d 0 is trivial: the only basis function b0,0 (t) is constant 1 and so(t) is thus constant po,0 for all t = [−1, 1]. ...9 The d+1 basis functions bd,k (t) form a ba- sis Bd {ba,o(t), ba,1(t), bd,d(t)} of the function space of all possible sα (t) functions. Clearly, you wish to find out, which of them given a particular maximal degree d is the best-possible approximation of f(t) in the least- squares sense. _ 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1 function f(t) = exp((2t)/3) - 1 to project -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5…arrow_forward
- An image processor considered a 750×750 pixels large subset of an image and converted it into gray-scale, resulting in matrix gIn - a false-color visualization of gIn is shown in the top-left below. He prepared a two-dim. box filter f1 as a 25×25 matrix with only the 5×5 values in the middle being non-zero – this filter is shown in the top-middle position below. He then convolved £1 with itself to get £2, before convolving £2 with itself to get f3. In both of the steps, he maintained the 25×25 size. Next, he convolved gIn with £3 to get gl. Which of the six panels below shows g1? Argue by explaining all the steps, so far: What did the image processor do when preparing ₤3? What image processing operation (from gin to g1) did he prepare and what's the effect that can be seen? Next, he convolved the rows of f3 with filter 1/2 (-1, 8, 0, -8, 1) to get f4 - you find a visualization of filter f 4 below. He then convolved gIn with f4 to get g2 and you can find the result shown below. What…arrow_forward3ur Colors are enchanting and elusive. A multitude of color systems has been proposed over a three-digits number of years - maybe more than the number of purposes that they serve... - Everyone knows the additive RGB color system – we usually serve light-emitting IT components like monitors with colors in that system. Here, we use c = (r, g, b) RGB with r, g, bЄ [0,1] to describe a color c. = T For printing, however, we usually use the subtractive CMY color system. The same color c becomes c = (c, m, y) CMY (1-c, 1-m, 1-y) RGB Note how we use subscripts to indicate with coordinate system the coordinates correspond to. Explain, why it is not possible to find a linear transformation between RGB and CMY coordinates. Farbenlehr c von Goethe Erster Band. Roſt einen Defte mit fergen up Tübingen, is et 3. Cotta'fden Babarblung. ISIO Homogeneous coordinates give us a work-around: If we specify colors in 4D, instead, with the 4th coordinate being the homogeneous coordinate h so that every actual…arrow_forwardCan someone provide an answer & detailed explanation please? Thank you kindly!arrow_forward
- Given the cubic function f(x) = x^3-6x^2 + 11x- 6, do the following: Plot the graph of the function. Find the critical points and determine whether each is a local minimum, local maximum, or a saddle point. Find the inflection point(s) (if any).Identify the intervals where the function is increasing and decreasing. Determine the end behavior of the graph.arrow_forwardGiven the quadratic function f(x) = x^2-4x+3, plot the graph of the function and find the following: The vertex of the parabola .The x-intercepts (if any). The y-intercept. Create graph also before solve.arrow_forwardwhat model best fits this dataarrow_forward
- Round as specified A) 257 down to the nearest 10’s place B) 650 to the nearest even hundreds, place C) 593 to the nearest 10’s place D) 4157 to the nearest hundreds, place E) 7126 to the nearest thousand place arrow_forwardEstimate the following products in two different ways and explain each method  A) 52x39 B) 17x74 C) 88x11 D) 26x42arrow_forwardFind a range estimate for these problems A) 57x1924 B) 1349x45 C) 547x73951arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning



