How Is the Resultant Force on a Car Calculated?

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To calculate the resultant force on a car pulling a trailer, the total mass of the system (car plus trailer) is considered, which is 1340 kg. Using the formula F = ma, the resultant force is determined to be 2827.4 N, directed forward. A free body diagram helps visualize the forces acting on the car, with components in both the x and y directions. The angle of the resultant force relative to the vertical is calculated to be 12.15 degrees. The discussion emphasizes the importance of considering the entire system's mass when calculating the horizontal component of the force.
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Homework Statement



A 1040 kg car is pulling a 300 kg trailer. Together the car and trailer move forward with an acceleration of 2.11 m/s2. Ignore any frictional force of air drag on the car and all frictional forces on the trailer. What is the resultant force exerted by the car on the road and in what direction (measured from the left of vertically downwards)?

Homework Equations



F = ma

The Attempt at a Solution



I already found the magnitude by making a free body diagram with the acceleration of the car going on the negative x axis, and the weight of the car on the negative y axis. then, i squared the values of the force in the y direction and x direction, added them together and took the square root of that, finding the force to be 10425. so now i tried doing the sin-1 of x component/y component and got theta to be 12.15 degrees.

i attached a paint version of my free body diagram. any help would be greatly appreciated.
 

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Recalculate the horizontal component (the friction force). Realize that the friction force must accelerate the entire system of both car and trailer.
 

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