Two forces are applied to a car in an effort to move it, as shown in the following figure, where F1 = 439 N and F2 = 365 N. (Assume up and to the right as positive directions.)
(a) What is the resultant of these two forces? magnitude___ N
direction ____° to the right of the forward direction
(b) If the car has a mass of 3,000 kg, what acceleration does it have? Ignore friction.
____ m/s2
without the picture, there is little hope.
To find the resultant of two forces, you can use the principles of vector addition. The resultant force is the vector sum of the individual forces.
(a) To find the magnitude of the resultant force, you can use the Pythagorean theorem:
Resultant Force Magnitude = √(F1^2 + F2^2)
Using the given values,
Resultant Force Magnitude = √((439 N)^2 + (365 N)^2) = √(193,121 N^2 + 133,225 N^2) = √(326,346 N^2) ≈ 571.17 N
To find the direction of the resultant force, you can use trigonometry. In this case, you can use the inverse tangent (arctan) function:
Resultant Force Direction = tan^(-1)(F2 / F1)
Using the given values,
Resultant Force Direction = tan^(-1)(365 N / 439 N) ≈ 42.23°
Therefore, the magnitude of the resultant force is approximately 571.17 N, and the direction is approximately 42.23° to the right of the forward direction.
(b) To find the acceleration of the car, you can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration:
Resultant Force = Mass × Acceleration
Rearranging the formula to solve for acceleration:
Acceleration = Resultant Force / Mass
Using the given values,
Acceleration = 571.17 N / 3,000 kg ≈ 0.19 m/s^2
Therefore, the car has an acceleration of approximately 0.19 m/s^2.