Two forces are applied to a car in an effort to accelerate it, as shown below. The first force, F1 = 364 N, is applied at an angle α = 33° to the forward dashed line. The second force, F2 = 522 N, is applied at an angle β = 11° to the forward dashed line.
What is the resultant of these two forces? N
If the car has a mass of 3050 kg, what acceleration does it have? (Disregard friction.)m/s2
To find the resultant of the two forces, we need to break each force into its horizontal and vertical components.
Let's start with the first force, F1 = 364 N at an angle α = 33°. To find the horizontal component, we can use the formula: Fx = F * cos(θ), where θ is the angle between the force and the horizontal axis.
Fx1 = 364 N * cos(33°) ≈ 303.35 N
To find the vertical component, we can use the formula: Fy = F * sin(θ).
Fy1 = 364 N * sin(33°) ≈ 194.77 N
Now let's do the same for the second force, F2 = 522 N at an angle β = 11°.
Fx2 = 522 N * cos(11°) ≈ 513.79 N
Fy2 = 522 N * sin(11°) ≈ 97.1 N
To find the resultant of the horizontal components, we add the horizontal components together:
Resultant horizontal component (Rx) = Fx1 + Fx2 ≈ 303.35 N + 513.79 N ≈ 817.14 N
To find the resultant of the vertical components, we add the vertical components together:
Resultant vertical component (Ry) = Fy1 + Fy2 ≈ 194.77 N + 97.1 N ≈ 291.87 N
Now we can find the magnitude of the resultant (R) using the Pythagorean theorem:
R = √(Rx^2 + Ry^2) ≈ √(817.14 N^2 + 291.87 N^2) ≈ √(670108.06 N^2) ≈ 818.16 N
So, the magnitude of the resultant of these two forces is approximately 818.16 N.
To find the acceleration of the car, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a): F = m * a.
R = m * a
a = R / m
Substituting the values we know:
a = 818.16 N / 3050 kg ≈ 0.268 m/s^2
Therefore, the car has an acceleration of approximately 0.268 m/s^2.