Two forces are applied to a car in an effort to move it, as shown in the following figure, where F1 = 443 N and F2 = 372 N. (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
if you understand interpolation, and you seem to, just think of it this way.
If the value you want is, say, 2/3 of the way from one known value to the next, the readings will also be 2/3 of the way from one value to the next.
so, if you want to place values at 1-unit intervals, you need to step through the given timestamps and whenever you find two timestamps greater than one unit apart, interpolate.
3 and 4.5 are greater than 1 unit apart, so, since 4 is 2/3 of the way between 3 and 4.5, you will generate values 2/3 of the way between those at 3, and those at 4.5.
Since 7 is more than 1 unit away from 4.5, you need to generate data points for times of 5 and 6.
5 is 1/5 of the way from 4 to 7.5
6 is 3/5 of the way.
so, given x-values and y-values,
if xn+1 - xn > 1,
for each number xk between xn and xn+1,
yk = yn + (xk-xn)/(xn+1-xn) * (yn+1-yn)
To find the resultant force, you need to combine the two given forces. The resultant force is the vector sum of the two forces.
(a) To find the magnitude of the resultant force, you can use the Pythagorean theorem:
Resultant force (magnitude) = √(F1^2 + F2^2)
= √(443^2 + 372^2)
= √(196,249 + 138,384)
= √334,633
≈ 578.34 N
To find the direction of the resultant force, you can use trigonometry. Since the forces are in the positive direction (up and to the right), the resultant force forms a right-angled triangle with the x and y components of the forces. The direction can be found using the inverse tangent function:
Resultant force (direction) = arctan(F2/F1)
= arctan(372/443)
≈ 42.92°
Therefore, the resultant force has a magnitude of approximately 578.34 N and is directed at an angle of approximately 42.92° to the right of the forward direction.
(b) To find the acceleration of the car, you can use Newton's second law of motion, which states that F = ma, where F is the force, m is the mass, and a is the acceleration.
Acceleration = Resultant force / Mass
= 578.34 N / 3,000 kg
≈ 0.193 m/s²
Therefore, the car has an acceleration of approximately 0.193 m/s².