Question

if the two forces shown in the diagram below are applied to the 2 kg ball, then what is the resulting acceleration of the ball?
frictionless surface
a 3.0 m/s² to the right
b 5.0 m/s² to the left
c 3.0 m/s² to the left
d 5.0 m/s² to the right

Explanation:

Step1: Calculate net force

Since the forces are in the same direction (both to the right), net force \(F_{net}=F_1 + F_2\).
\(F_{net}=2.0\,\text{N}+8.0\,\text{N}=10.0\,\text{N}\) (to the right)

Step2: Use Newton's second law \(F = ma\) to find acceleration

We know \(F_{net}=ma\), so \(a=\frac{F_{net}}{m}\).
Given \(m = 2\,\text{kg}\), \(a=\frac{10.0\,\text{N}}{2\,\text{kg}} = 5.0\,\text{m/s}^2\). Direction is same as net force (to the right).

Answer:

d \(5.0\,\text{m/s}^2\) to the right