Two forces are applied to a car in an effort to accelerate it. The first force, F1 = 326 N, is applied at an angle α = 40° to the forward dashed line. The second force, F2 = 488 N, is applied at an angle β = 8° to the forward dashed line.
a. What is the resultant of these two forces?
blank N at blank degrees.
If the car has a mass of 2900 kg, what acceleration does it have? (Disregard friction.)
blank m/s^2 at blank degrees
90
To find the resultant of the two forces, we can use vector addition.
Step 1: Convert the forces into their x and y components.
- Force F1:
- F1x = F1 * cos(α)
- F1y = F1 * sin(α)
- Force F2:
- F2x = F2 * cos(β)
- F2y = F2 * sin(β)
Step 2: Add the x and y components separately to find the overall x and y components of the resultant.
- Resultant force in the x-direction: Rx = F1x + F2x
- Resultant force in the y-direction: Ry = F1y + F2y
Step 3: Find the magnitude and direction of the resultant.
- Magnitude: R = sqrt(Rx^2 + Ry^2)
- Direction: θ = atan(Ry / Rx)
Step 4: Calculate the acceleration of the car using Newton's second law.
- Newton's second law: F = m * a, where F is the resultant force and m is the mass of the car.
- Acceleration: a = F / m
Let's calculate the answers:
a. Resultant of the two forces:
- Calculate the x and y components of forces F1 and F2:
- F1x = 326 N * cos(40°)
- F1y = 326 N * sin(40°)
- F2x = 488 N * cos(8°)
- F2y = 488 N * sin(8°)
- Add the x and y components:
- Rx = F1x + F2x
- Ry = F1y + F2y
- Calculate the magnitude and direction:
- R = sqrt(Rx^2 + Ry^2)
- θ = atan(Ry / Rx)
b. Acceleration of the car:
- Calculate the acceleration using Newton's second law:
- F = R (resultant force)
- a = F / m (mass of the car)
Now, let's substitute the values into the above equations to find the answers.