Example Problem with Complete Solution

1B-2: Mass, Force and Acceleration 4 pts
A 5 kg rock is thrown upward with a force of 150 N at a location where the local gravitational acceleration is 9.79 m/s2. Determine the acceleration of the rock in m/s2.
Read : The key here is to recognize that two forces are acting on the rock: the 150 N and the weight of the rock (due to gravity).  Then, the problem becomes an application of Newton's 1st Law of Motion.
Given : m 5 kg
Fthrow 150 N
g 9.79 m/s2
Find : a ??? m/s2
Solution : The key equation here is Newton's 1st Law of Motion : eqn-1
Eqn 1
We can solve Eqn 1 for the rate at which the rock accelerates :
eqn-2
Eqn 2
We know that : gC 1 kg-m/N-s2
eqn-3
So, all we need to is determine the net force acting on the stone.
A free-body diagram might be helpful.
The net force acting on the rock in the upward direction is :
eqn-4
Eqn 3
We can apply Newton's 1st Law of
 Motion again to evaluate Fwt.		 eqn-5eqn-6
Eqn 4
We can solve Eqn 4 for Fwt, as follows : Eqn 5
Plugging values into Eqn 5, then Eqn 3 and, finally, Eqn 2 yields :
Fwt 49.0 N
Fnet 101.05 N
a 20.21 m/s2
Answers : a 20.2 m/s2