Question

Two forces are applied to a car in an effort to accelerate it, as shown below. The first force, F1 = 382 N, is applied at an angle = 32° to the forward dashed line. The second force, F2 = 500 N, is applied at an angle = 15° to the forward dashed line.

(a) What is the resultant of these two forces?

_ N at _ ° to the right of the forward dashed line

(b) If the car has a mass of 3050 kg, what acceleration does it have? (Disregard friction.)

_ m/s2 at _ ° to the left of the forward dashed line

Answer 1

The resultant of two applied forces on a car is 874.59 N at an angle of 22.35° to the right of the forward dashed line. If the car has a mass of 3050 kg and friction is disregarded, the car will accelerate at 0.287 m/s² in the same direction as the resultant force.

Step-by-step explanation:

To determine the resultant of the two forces applied to the car, we can use vector addition. Each force can be broken down into horizontal and vertical components using trigonometric functions.

The components of F1 are:
Horizontal (F1x) = F1 * cos(θ) = 382 N * cos(32°) = 323.88 N
Vertical (F1y) = F1 * sin(θ) = 382 N * sin(32°) = 202.01 N

The components of F2 are:
Horizontal (F2x) = F2 * cos(θ) = 500 N * cos(15°) = 483.02 N
Vertical (F2y) = F2 * sin(θ) = 500 N * sin(15°) = 129.41 N

The total horizontal and vertical components are:
Horizontal (Fx_total) = F1x + F2x = 323.88 N + 483.02 N = 806.90 N
Vertical (Fy_total) = F1y + F2y = 202.01 N + 129.41 N = 331.42 N

Now, to find the magnitude of the resultant force (FR):
FR = √(Fx_total² + Fy_total²) = √(806.90 N² + 331.42 N²) = 874.59 N

And to find the direction of the resultant force with respect to the forward dashed line:
α = tan⁻¹(Fy_total/Fx_total) = tan⁻¹(331.42 N/806.90 N) = 22.35°

For the acceleration:
Newton's second law states F = ma, so to find the acceleration a = F/m we use the resultant force FR.
a = FR / m = 874.59 N / 3050 kg = 0.287 m/s²

The direction of the acceleration is the same as the direction of the resultant force, which is 22.35° to the right of the forward dashed line, since we have disregarded friction.