A strong boy throws a rock
straight up with a force of 100 N. At what rate does the rock initially accelerate upwards, in m/s^{2}? Assume the mass of the rock is 2 kg and the local gravitational
acceleration is 9.74
m/s^{2}. 


Read: 
The key here is to
recognize that two forces are acting on the rock: the 100
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 
2 
kg 



g 
9.74 
m/s^{2} 

F_{throw} 
100 
N 
















Find: 
a 
??? 
m/s^{2} 
















Assumptions: 
None. 

















Equations
/ Data / Solve: 


















The key equation here
is Newton's 1st Law of Motion : 


Eqn 1 











We can solve Eqn 1 for the rate at which the
rock accelerates : 





Eqn 2 











We know that : 




g_{C} 
1 
kgm/Ns^{2} 











So, all we need to is
determine the net force acting on the stone. 













A freebody diagram
might be helpful. 












The net force acting
on the rock in the upward
direction is : 













Eqn 3 













We can apply Newton's
1st Law of
Motion again to evaluate F_{wt}. 




Eqn 4 











We can solve Eqn 4 for F_{wt}, as follows : 



Eqn 5 











Plugging
values into Eqn 5, then Eqn 3 and, finally, Eqn 2 yields : 


F_{wt} 
19.5 
N 



F_{net} 
80.52 
N 







a 
40.26 
m/s^{2} 










Answers: 
a 
40.3 
m/s^{2} 















