(a)
units of axy = N
unit of x , y = m
a*m*m = kg m /s^2
a = kg m^-1 s^-2
unit of by = N
b*m = kg m s-2
b = kg s-2
=======================
(b)
from origin to (5,0)
along this line y = 0
F = 0
W = 0
towards north
x = 5
F = 7*5*y i + 4y j
F = 30y i + 4y j
work = F.r
r = yj
W = 4y^2 J = 4*3^2 J
W = 36 J
Wtotal = 36 J
================
(c)
towards north
x = 0
F = by j = 4y j
r = y j
W = F.r = 4y^2 J
W = 4*3^2 = 36 J
towards east
y = 3
F = 21x i + 12 j
r = xi
W = 21x^2 J
W = 21*5^2 = 525 J
Wtotal = 561 J
An object moves across a level, frictionless surface marked with a set of x-y axes, with...
(a) A force F = (5xî + 4yĵ), where F is in newtons and x and y are in meters, acts on an object as the object moves in the x-direction from the origin to x = 5.21 m. Find the work W = F · dr done by the force on the object (in J). J (b) What If? Find the work W = F · dr done by the force on the object (in J) if it moves...
The force field F (x, y) = (x + 4y)i + (x^2 − 3)j acts on an object traveling from (0, 0) to (0, 1). The object moves along the path x = c(y − y^2 ) with 0 ≤ y ≤ 1. Determine the value of c that minimizes the work done on the object by the force field. Please use the line work integral, and optimization
The x component of a di nt vector r is-145 m, while its y is -176 m. (a) Find the magnitude of 228 0 b) Find the direction of r. 144 11 1 WA 044 A golfer takes three strokes to putt a golf ball into a hole. On the first stroke, the ball moves 5.2 m dure east. On the second, moves 2.0 m at an angle 2ot north of east On the sird moves 0.50 m due north....
and positive z pointing out of the page. A rectangular box sits aligned with the x, y, and z axes, with one corner at the origin, and the opposite corner at < 0.5, 0.4, 0.3 > meters. (In other words, the box is 0.5 meters long in the x direction, 0.4 meters tall in the y direction, and 0.3 meters deep in the z direction). Along the left side of the box (the part on the y-z plane), the electric...
DIFFERENTIAL EQUATION PROBLEM An object with a mass of 2 kg moves along the x-axis and we will assume that the positive direction of movement is to the right. Only one force (in N) is present and opposes the movement. Let be the speed of the object (in m / s) at time t. The object starts from the origin (x = 0) with an initial speed of 75 m / s. Suppose that the resistance force has a magnitude...
please show work thank you An object moves along the y-axis (marked in feet) so that its position at time x (in seconds) is given by the function f(x) = x3 – 15x² + 72x. a. Find the instantaneous velocity function v= v = f'(x). b. Find the velocity when x= 1. c. Find the time(s) when v=0. a. V= b. The velocity of the object at x= 1 is ft/s. (Simplify your answer.) c. The velocity is zero at...
physics - te ca y Averach A force of magnitude 7.10 units acts on an object at the origin in a direction = 34.0 above the positive x-axis. (See the figure below.) A second force, of magnitude 5.00 units acts on the object in the direction of the positive y-axis. Find graphically the magnitude and direction of the resultant force poros SC . Orch A man in a maze makes three consecutive displacements. His first displacement is 8.60 m westward,...
1. Suppose an object is subjected to a force F that varies with position: where β 20N/m is a constant. a) The object begins at the origin (x,y) = (0,0) and travels to point P located at (z,y)-(1m,3m): 3m 4m Calculate the work done by F along each of the three possible paths shown in the figure above by the dashed lines. Note that there could be other forces acting on the object in order to ensure the object travels...
You and a friend both purchase dune buggies. These off-road vehicles are excellent for driving on sand. To test out your new rides, you decide to play a game of cat and mouse in a desert with sand dunes. Both of you start in the same location. You give your friend a head start, then attempt to catch up teo them. To give you a chance, they radio you their coordinates several times You may assume that both dune buggies...
1. ( 8 points) An object moves though a vector field, \(\overrightarrow{\mathbf{F}}(x, y)\), along a circular path, \(\overrightarrow{\mathbf{r}}(t)\), starting at \(P\) and ending at \(Q\) as shown in the graph below.(a) At the point \(R\) draw and label a tangent vector in the direction of \(d \overrightarrow{\mathbf{r}}\).(b) At the point \(R\) draw and label a vector in the direction of the vector filed, \(\overrightarrow{\mathbf{F}}(R)\).(c) At the point \(R\) is \(\overrightarrow{\mathbf{F}} \cdot d \overrightarrow{\mathbf{r}}\) positive, negative, or zero? Circle the correct...