Question

A 2 kg mass is free falling in the negative Y direction when a 10 N force is exerted in the minus X direction. What is the acceleration of the mass?

Answer 1

Answer:

The mass's acceleration is 5 m/s^2 in the minus X direction and 9,8 m/s^2 in the minus Y direction.

Explanation:

By applying the second Newton's law in the X and Y direction we found that in the minus X direction an external force of 10 N is exerted, while in the minus Y direction the gravity acceleration is acting:

X-direction balance force: $-10 [N] = m.ax$

Y-direction balance force: $-m*9,8 \frac{m}{s^2} = m.ay$

Where ax and ay are the components of the respective acceleration and m is the mass. By solving for each acceleration:

$ax=(-10 [N]) / m$

$ay=-m*9,8\frac{m}{s^2} / m$

Note that for the second equation above the mass is cancelled and, the Y direction acceleration is minus the gravity acceleration:

$ay=-9,8\frac{m}{s^2}$

For the x component aceleration we must replace the Newton unit:

$N =\frac{kg.m}{s^2}$

$ax= -10 \frac{kg.m}{s^2} / (2 kg)$

$ax= - 5 \frac{m}{s^2}$