Your car is stuck in the mud and two friends are helping you. One is pulling on your car with a force of 370 N at a 40 degree angle and the other is pulling with a force of 450 N at a 30 degree angle. A force of 725 N is required to remove the car. Is the car still stuck? Please show me how to arrive at the answer.
F = 370 N @ 40 deg. + 450 N @ 30 deg.
X = hor = 370 * cos40 + 450 * cos30,
= 283.4 + 389.7 = 673.1 N.
Y = ver = 370 * sin40 + 450 * sin30,
= 237.8 + 225 = 462.8 N.
tanA = Y/X = 462.8 / 673.1 = 0.6876,
A = 34.5 deg.
F = X / cosA = 673.1/cos34.5 = 816.7N.
816.7 N > 725 N.
Therefore, the car is no longer stuck.
X and Y represent the hor and ver side of a rt triangle and F is the hyp
or Resultant.
To determine if the car is still stuck, we can calculate the total force exerted on the car by summing up the forces applied by each friend.
Let's start by resolving the forces applied by each friend into horizontal and vertical components. We can use trigonometry to find these components.
Friend 1 is pulling with a force of 370 N at a 40 degree angle. The horizontal component, F1x, is given by F1 * cos(angle) and the vertical component, F1y, is given by F1 * sin(angle).
F1x = 370 N * cos(40°) = 282.662 N
F1y = 370 N * sin(40°) = 236.426 N
Similarly, for Friend 2:
F2x = 450 N * cos(30°) = 389.711 N
F2y = 450 N * sin(30°) = 225 N
Now, let's calculate the total horizontal force (F_total_x) and vertical force (F_total_y) applied to the car by adding the respective components:
F_total_x = F1x + F2x = 282.662 N + 389.711 N = 672.373 N
F_total_y = F1y + F2y = 236.426 N + 225 N = 461.426 N
Next, we can calculate the magnitude of the total force (F_total) applied to the car using the Pythagorean theorem:
F_total = √(F_total_x^2 + F_total_y^2) = √(672.373 N^2 + 461.426 N^2) = √(455898.601 N^2) = 675.89 N
From the calculations, we can see that the total force applied to the car is approximately 675.89 N. Since this force is less than the 725 N required to remove the car, the car is still stuck in the mud.
Therefore, the car is still stuck, and you would need additional force to remove it from the mud.