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

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.

Step-by-step 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 (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(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(m)/(s^2)`

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

`N =(kg.m)/(s^2)`

`ax= -10 (kg.m)/(s^2) / (2 kg)`

`ax= - 5 (m)/(s^2)`