If the 1kg standard body is accelerated by only f1=(3.o)+(4.0) and f2=(-2.0)+(-6.0) then what is fnet(al in unit vector notation and as (b) magnitude and (c) an angle relative to the positive x direction? what are the (d) magnitude and (e) angle of a ?

(a)

The two forces are:

To calculate the net force, we must calculate the resultant of the two vectors, which is obtained by separately summing the components of each vector:

So, the net force is

(b) 2.24 N

The magnitude of the net force is given by the Pythagorean theorem: it is equal to the square root of the sum of the squares of the single components:

(c)

The angle of the net force, relative to the positive x direction, is equal to the arctangent of the ratio between the vertical component and the horizontal component:

(d) 2.24 m/s^2

The mass of the object is m = 1 kg, so according to Newton's second law the acceleration is given by

Since we are interested in the magnitude of the acceleration, we have to take the magnitude of the net force into the calculation:

(e)

According to Newton's second law:

The acceleration has the same direction of the force, therefore the angle of the acceleration (measured with respect to the positive x direction) is .

what was the acceleration of the 2 kg cart?

⇒ 16.0 cm/s2

what was the acceleration of the 4 kg cart?

⇒ 8.1 cm/s2

what was the acceleration of the 6 kg cart?

⇒ 5.3 cm/s2