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/s2? Assume the mass of the rock is 2 kg and the local gravitational
acceleration is 9.74
m/s2. |
|
|
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/s2 |
|
Fthrow |
100 |
N |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Find: |
a |
??? |
m/s2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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 : |
|
|
|
|
gC |
1 |
kg-m/N-s2 |
|
|
|
|
|
|
|
|
|
|
|
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 3 |
|
|
|
|
|
|
|
|
|
|
|
|
|
We can apply Newton's
1st Law of
Motion again to evaluate Fwt. |
|
|
|
|
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 |
19.5 |
N |
|
|
|
Fnet |
80.52 |
N |
|
|
|
|
|
|
|
a |
40.26 |
m/s2 |
|
|
|
|
|
|
|
|
|
|
Answers: |
a |
40.3 |
m/s2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|