Question

Two forces are applied to a car in an effort to accelerate it, as shown below.
a. What is the resultant of these two forces?
b. If the car has a mass of 3200 kg, what acceleration
does it have? (Disregard friction.)

Answer 1

The resultant of these two forces is 780.31N

If the car has a mass of 3200 kg, the acceleration of the car is 0.244m/s²

The formula for the resultant force is expressed as:

$R =\sqrt{(\sum F_x)^2+(\sum F_y)^2}$

Take the sum of force along the horizontal

$\sum F_x = 450cos10^0+380cos30^0\\\sum F_x =443.16 + 329.09\\\sum F_x = 772.25N$

Take the sum of force along the vertical

$\sum F_y = 450sin10^0-380sin30^0\\\sum F_y=78.14 - 190\\\sum F_y= -111.86N$

Get the resultant force:

$R =\sqrt{(772.25)^2+(-111.86)^2}\\R = \sqrt{596,370.0625 +12,512.6596}\\R = \sqrt{608,882.7221}\\R = 780.31N$

Hence the resultant of these two forces is 780.31N

b) According to Newton's second law of motion;

$R =ma\\a=\frac{R}{m} \\a=\frac{780.31}{3200}\\a = 0.244m/s^2$

Hence If the car has a mass of 3200 kg, the acceleration of the car is 0.244m/s²

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