Gen Physics Vector Force example problem

Gen Physics Vector Force example problem

1. Three vector forces; F,, F,,and F; , acton a
particle of mass m= 1.73 kg as shown in the figure.

1.Calculate the
magnitude and
direction of the net
force acting on the
particle.

2.Calculate the particle’s
acceleration.

2. Step 1 of 3
+ Get the x and y components of the forces.

F,= F, (note the quadrant of x) + F> + Fs
F,= -20c0s36° + 50 + 30cos45°
F,= 55.033 N

F,= F, + F> (no y component) # F. ‘3 (note the quadrant of y)
F,= 20sin36° + 0 - 30cos45°
F,=-9.46 N

:. We can now assume from the given net forces that the
net force is located at quadrant 4 (positive x, negative y).

3. Step 2 of 3
1. Magnitude and direction of the net force acting on the particle.

+ Free= | (EJ? + (F,) = (65.033 N)? + (-9.46 N ?
= /3,028.631 N? + 89.492 N? = 55.840 N

Ey 9.46N

E, 55.0830 0272
* 9 = tan-1(0.172) = 9.7590

* tan0 =

:. The net force has a magnitude of 55.840 N and is
located 9.759° below the positive x axis (quadrant 4).

4. 2. Calculate the particle’s acceleration.

m
Fret 55.840 N 55.840 kz
=
° : 1.73 kg 1.73 kg