Question

To calculate the normal and tangential components of the acceleration of an object along a given path.

A particle is traveling along the path y(x)=0.2x2y(x)=0.2x2, as shown in (Figure 1), where yy is in meters when xx is in meters. When xxx = 7 mm , the particle's velocity is vvv = 10 m/sm/s and the magnitude of its acceleration is aaam = 4 m/s2m/s2 . Determine the normal and tangential components of the acceleration.

Item 10 Learning Goal: To calculate the normal and tangential components of the acceleration of an object along a given path. Part A What is the angle between the positive 2-axis and the unit tangent vector for the motion at x = 7 m ? Express your answer to three significant figures with appropriate units. A particle is traveling along the path y(x) = 0.2c", as shown in (Figure 1), where y is in meters when x is in meters. When 2 = 7 m, the particle's velocity is v = 10 m/s and the magnitude of its acceleration is a = 4 m/s. Determine the normal and tangential components of the acceleration. View Available Hint(s) THÅR O O ? Figure < 1 of 1 > Value Units Submit Part B What is the radius of curvature of the path at 3 = 7 m ? Express your answer to three significant figures with appropriate units. View Available Hint(s)

Answer 1

v=10m/s ; a=4m/6² da @ 9=7 = (23) = (0+2) = 2.8 ฝ่1 tan A=28 4 0= 70-346 Part A - angle b/w stoxis and mit tangent vector G = 70.346 kout B Rodius of curvature for R = [1+ (y'(x) 21 312 parabola y'(x) = .4x g'(x) = 04 R = 1+ 16x2 = 65.708 m

Partice Magnitude of normal accelera a = 10² = 1.52188 m/s² 65.708 Port D direction of an from x-axis el = goto a = 90+ 7 0.346 @ = 160-346. Port E OR = azta? ap = 4 m/s² = Va{+ (1.523² - q = 3.699 m/s²