Two forces are applied to a car in an effort to accelerate it, as shown below. The first force, F1 = 400 N, is applied at an angle α = 32° to the forward dashed line. The second force, F2 = 536 N, is applied at an angle β = 10° 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 2900 kg, what acceleration does it have? (Disregard friction.)
m/s2 at ° to the right
See previous post: Sat, 12-6-14, 4:06 PM
To find the resultant of the two forces, we can use vector addition. The resultant is the vector sum of the individual forces.
(a) To find the resultant, we need to break the forces into their x and y components. The x-component of a force is the force multiplied by the cosine of the angle, and the y-component is the force multiplied by the sine of the angle.
For the first force, F1 = 400 N at an angle α = 32°:
F1x = F1 * cos(α)
F1y = F1 * sin(α)
For the second force, F2 = 536 N at an angle β = 10°:
F2x = F2 * cos(β)
F2y = F2 * sin(β)
Once we have the x and y components, we can find the resultant. The x-component of the resultant is the sum of the x-components of the forces, and the y-component of the resultant is the sum of the y-components of the forces.
Rx = F1x + F2x
Ry = F1y + F2y
The magnitude of the resultant is calculated using the Pythagorean theorem:
R = sqrt(Rx^2 + Ry^2)
To find the angle of the resultant, we can use trigonometry. The angle is given by:
θ = arctan(Ry/Rx)
Now we can substitute the values into the equations to find the resultant.
(b) To find the acceleration of the car, we can use Newton's second law, which states that the net force acting on an object is equal to its mass multiplied by its acceleration.
The net force is the magnitude of the resultant force:
Net force = R
So, the acceleration of the car is given by:
Acceleration = Net force / Mass
Substitute the values to find the acceleration.