A particle moving in the x-y plane has a position vector given by r- 1.67t2i+1.44t³j, where r is in inches and t is in seconds. Calculate the radius of curvature p of the path for the position of the particle when t- 1.9 sec. Sketch the velocity v and the curvature of the path for this particular instant. Answer:p-i in.
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- An object moving at constant speed v around a circle of radius rhas an acceleration a directed toward the center of the circle. The SI unit of acceleration is m/s2. If the speed is increased 16.5%, by what percentage does the radial acceleration increase?A particle moves ccw on a circular path of 400 ft radius. It starts from a fixed point which is horizontally to the right of the center of the path and moves so that s = 10t2 + 20t where s is the arc distance in ft and t is the time in sec. Compute the x and y components of the acceleration at the end of 3 seconds.A particle moving in the x-y plane has a position vector given by r = 1.12t²i + 1.30t³j, where r is in inches and t is in seconds. Calculate the radius of curvature p of the path for the position of the particle when t = 2.5 sec. Sketch the velocity v and the curvature of the path for this particular instant. Answer: p= i eTextbook and Media in.
- The speed of a particle moving along a circle of radius r= 4 m, is v(t) = 4t; where v is in m/s and t is in s. The magnitude of the total acceleration (in m/s-) of the particle st st 1 10 a. 2.15. A particle moves counterclockwise on a circular path of 400 ft radius. It starts from a fixed point which is horizontally to the right of the center of the path and moves so that s=1012 + 20t where s is the arc distance in feet and t is the time in sec. Compute the x and y components of acceleration at the end of 3 sec.The magnitu A (2.0i + 2.0j) m Solution You may wish to draw the vectors to conceptualize - (2.01 - 4.0) m and B = the situation. We calegorize this as a simple plug-in problem. Comparing this expression for A with the general expres- sion A A, i + A,j, we see that A= 2.0 m and A, = 2.0 m. We can fir = - 4.0 m. We obtain the resul- = 2.0 m and B Likewise, B tant vector R, using Equation 3.14: R = A + B = (2.0 + 2.0) i m + (2.0 – 4.0)f m (4.0i – 2.0j) m Your c tan %3D mean been or = 4.0 m R, = - 2.0 m the + Example 3.4 The Resultant Displacement Your A particle undergoes three consecutive displacements: the c (15i + 30j + 12k) cm, d = (23i – 14j - 5.0k) cn %3D O Cm, di %3D and dg = (-- 13i + 15j) cm. Find the components of the resultant displacement and its magnitude. %3D sion to th on Three-dinmensional displacements are more diffi- imagine than those in two dimensions, because the can be drawn on paper. For this problem, let us concep- e that you start with your pencil at the origin of…
- A particle moving in the x-y plane has a position vector given by r = 0.81t²i + 0.74t³j, where r is in inches and t is in seconds. Calculate the radius of curvature p of the path for the position of the particle when t = 2.1 sec. Sketch the velocity v and the curvature of the path for this particular instant. Answer: p= i in.The acceleration due to gravity, g, is constant at sea level on the Earth's surface. However, the acceleration decreases as an object moves away from the Earth's surface due to the increase in distance from the center of the Earth. Derive an expression for the acceleration due to gravity at a distance h above the surface of the Earth, gh. Express the equation in terms of the radius R of the Earth, g, and h. 8h = Suppose a 70.00 kg hiker has ascended to a height of 1815 m above sea level in the process of climbing Mt. Washington. By what percent has the hiker's weight changed from its value at sea level as a result of climbing to this elevation? Use g = 9.807 m/s² and R = 6.371 × 106 m. Enter your answer as a positive value. weight change = %A ball swings counterclockwise in a vertical circle at the end of a rope 1.32 m long. When the ball is 36.3° past the lowest point on its way up, its total acceleration is (-20.2Î + 27.5)) m/s2. For that Instant, do the following. (a) Sketch a vector diagram showing the components of its acceleration. Browse... No file selected.
- A car P travels along a straight road with a constant speed v = 79 mi/hr. At the instant when the angle 0 = 69°, determine the values of r in ft/sec and 0 in deg/sec. Assume/= 130! Answers: r = 0 = i i 18 Ma V. ft/sec deg/secAn object moving at constant speed v around a circle of radius r has an acceleration a directed toward the center of the circle. The SI unit of acceleration is m/s2. If the speed is increased 19.0%, by what percentage does the radial acceleration increase?A particle moves clockwise in a circular path of 400 ft radius. It starts from a fixed point which is vertically at the top of the center of the path and moves so that s = 10t2 + 20t where s is the arc distance in ft and t is the time in sec. Compute the (a) velocity at the end of 4 sec. (b) x and y components of the acceleration at the end of 4 seconds. Skecth the motion of the particle and show the velocity and the x and y components of acceleration of the particle at the end of 4 sec.