What is the magnitude of an object\'s average velocity if an object moves from a
ID: 1368416 • Letter: W
Question
What is the magnitude of an object's average velocity if an object moves from a point with coordinates x = 2.5 m, y = -2.7 m to a point with coordinates x = 5.3 m, y = -9.3 m in a time interval of 2.5 s? A man in search of his dog drives first 11 mi northeast, then 32 mi straight south, and finally 1 mi in a direction 30 degree north of west. What are the magnitude and direction of his resultant displacement? The gravitational acceleration on the Moon is a sixth of that on Earth. The weight of a rock is 7.65 N on Earth. What is the weight of the rock on the Moon? What is the mass of the rock? A 421.5-N force accelerates a go-cart and its driver from 10.6 m/s to 17.8 m/s in 4.80 s. What is the mass of the go-cart plus driver? An elevator cabin has a mass of 378.7 kg, and the combined mass of the people inside the cabin is 166.4 kg. The cabin is pulled upward by a cable, with a constant acceleration of 2.53 m/s^2. What is the tension in the cable? An elevator cabin has a mass of 362.4 kg, and the combined mass of the people inside the cabin is 181 kg. The cabin is pulled upward by a cable, in which there is a tension force of 7635 N. What is the acceleration of the elevator ?Explanation / Answer
(1)
x1 = 2.5 m, y1 =-2.7 m , x2 =5.3 m, y2 = -9.3 m , t =2.5 s
Average velocity V= [(x2-x1)/t] i + [(y2-y1)/t] j
v = [ (5.3-2.5)/2.5] i + [ (-9.3 +2.7)/2.5 ] j
v = 1.12 i - 2.64 j
Magnitude of v = [(1.12)^2 + (-2.64)^2 ]^1/2
v = 2.86 m/s
(2) d1 = 11cos(45) i+11 sin(45) j
d1 = 7.78 i+7.78 j
d2 = - 32 j
d3 = -1 cos(30)i +1 sin(30)
d3 = - 0.87i +0.5 j
d =d1+d2+d3 = [7.78i +7.78j] +[-32j] +[-0.87i +0.5j]
d = 6.91i -23.72j
Magnitude of resultant diplacement d = [(6.91)^2 +(-23.72)^2]^1/2
d = 24.7 mi
tan(theta) = 23.72/6.91 [it is third coordinate]
theta = 73.7degress south of east
(3) gm =g/6 , g =9.8 m/s^2
w = 7.65
(a) wm = w/6 = 7.65/6 =1.275 N
(b) w = mg
m = w/g = 7.65/9.8 = 0.781 kg
(4) f =421.5 n , V1 =10.6 m/s , v2 =17.8 m/s , t = 4.8 s
a =(v2-v1)/t =(17.8 - 10.6)/4.8
a = 1.5 m/s^2
F =ma
m =F/a = 421.5/ 1.5 = 281 kg
5) M = 378.7 kg, m =166.4 kg, a =2.53 m/s^2
T -(M+m)g =(M+m)a
T = (M+m)(a+g)
T = (378.7+166.4) (9.8+2.53)
T = 6721.1 N
6) M = 362.4 kg, m =181 kg, T = 7635 N
T -(M+m)g =(M+m)a
7635 - (362.4+181)*9.8 = (362.4+181)a
a =4.25 m/s^2
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