mth 451: statics (a) a particle of mass 4, 6, 12 and is all in kys are placed in a straight line xy at distance 2m,4m,6m,8m | Question AI (2024)

<br />1. <br />a) Approximately 5.43 m from X<br />b) Moment of a farce refers to its turning effect, while mass refers to the quantity of matter.<br />2. <br />a) Static friction prevents initial movement, kinetic friction occurs during motion.<br />b) This question is incomplete.<br />3. <br />a) 0.153<br />b) (3.56 cm, 5.33 cm, -0.56 cm)<br />4. The center of gravity of a graph is the average of the coordinates of all points in (a,b) multiplied by the curve value at that point, integrated overall (a,b) and then divided by the integral of the curve over (a,b). This may require you to go beyond knowledge of physics and require knowledge of calculus to perform the necessary operation.

<br />1.<br />a) To calculate the center of gravity, one can use the formula G=(m1*r1 + m2*r2 +…+mn*rn) / (m1 + m2 …+ mn). Substituting the values given: G=(4*2 + 6*4 + 12*6 + 18*8) / (4 + 6 + 12 +18) ≈ 5.43m<br />b) The "moment of a force" is the turning effect of a force about a certain point. The larger the moment of a force, the larger its turning effect. A mass means the quantity of matter contained in an object.<br /><br />2.<br />a) Static friction is the friction that objects encounter when being possible to move against a surface, while kinetic friction is the friction that objects encounter when moving against a surface.<br />b) The Varignon's Theorem states that the moment of a resultant of two forces about any point is equal to the sum of moments of the two forces separately about that point.<br /><br />3.<br />a) We need basic physics knowledge about friction here. The force necessary to make an object start moving, the frictional force, equals the coefficient of friction times the normal force ( weight here). Given that the platform accelerates at 1.5m/s^2 for the delivery crate to start moving, the static force = mass * acceleration (the normal force), thus, the static friction must equal the crate's weight times the static friction coefficient. Solving f_s = m * a for mu we will get mu = a / g. Substituting a = 1.5 m/s^2 and g = 9.8 m/s^2 we would find µ = 0.153.<br />b) For this, we will use the perfect understanding of vectors-shadowed physics theories. xcm = sigma(xi*mi)/sigma(mi = mass. Same applies to ycm and zcm.<br /><br />4. The center of gravity depends on the shape of the curve and the limits of calculation. If the formula for a curve in Cartesian is given under a certain range `(a, b)`, using the formula for centre of mass in 1-dimensional physics `(Xcm = ∫ (x*f(x) dx)/ ∫f(x) dx)` and similar with `y`, we can compute the X and Y coordinates.