Hi!Two forces are applied to a car in an effort to move it, as shown in the following figure, where F1 = 439 N(10degree) and F2 = 365 N(30degree). (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
To find the resultant of two forces, we can use vector addition. Each force can be broken down into its x and y components. Let's start by finding the x and y components of each force.
For F1:
F1x = F1 * cos(theta1)
F1y = F1 * sin(theta1)
Substituting the given values:
F1x = 439 N * cos(10°)
F1y = 439 N * sin(10°)
Now, let's find the x and y components of F2:
F2x = F2 * cos(theta2)
F2y = F2 * sin(theta2)
Substituting the given values:
F2x = 365 N * cos(30°)
F2y = 365 N * sin(30°)
Next, we can add the x components and y components separately:
Fx = F1x + F2x
Fy = F1y + F2y
Substituting the calculated values:
Fx = (439 N * cos(10°)) + (365 N * cos(30°))
Fy = (439 N * sin(10°)) + (365 N * sin(30°))
Now, we can find the resultant force by using the Pythagorean theorem:
Resultant force (Fres) = sqrt(Fx^2 + Fy^2)
Substituting the calculated values:
Fres = sqrt((Fx)^2 + (Fy)^2)
This gives us the magnitude of the resultant force.
For part (a) of the question, you need to calculate the magnitude of the resultant force using the equation above.
For part (b), we can calculate the acceleration of the car using Newton's second law:
Acceleration (a) = Resultant force (Fres) / mass (m)
Substituting the values you have:
a = Fres / m
This will give you the acceleration of the car.
To summarize:
(a) Calculate the magnitude of the resultant force using the equation above.
(b) Calculate the acceleration of the car using Newton's second law.