Thread: defferential equation or physics

a long very smooth board is inclined at an angle of 10 degrees with the horizontal.A 10 kg. weights starts from rest 10 meter from the bottom of the board and slides downward under the action of gravity alone.
a.)find how long it will take the weight to reach the bottom of the board and with what velocity?

Originally Posted by alderon

a long very smooth board is inclined at an angle of 10 degrees with the horizontal.A 10 kg. weights starts from rest 10 meter from the bottom of the board and slides downward under the action of gravity alone.
a.)find how long it will take the weight to reach the bottom of the board and with what velocity?

Hello,

if I understand your problem correctly then there isn'r any friction involved(?). If so:
A mass of 10 kg has a weight of 98.1 N
the driving force which causes the acceleration is: $\displaystyle F=m \cdot \sin(10^\circ)$. With your data $\displaystyle F \approx 17.035~N$

1. $\displaystyle F=m \cdot a$. Using the given numbers:

$\displaystyle 17.035~N = 10~kg \cdot a~\Longrightarrow~ \boxed{a = 1.7035~\frac{m}{s^2}}$

2. $\displaystyle d=\frac{1}{2} \cdot a \cdot t^2$ . Using the given numbers:

$\displaystyle 10 = \frac{1}{2} \cdot 1.7035 ~\frac{m}{s^2} \cdot t^2 ~\Longrightarrow ~ \boxed{t\approx 3.426~s}$

3. $\displaystyle v = a \cdot t$. Plug in the knowns values:

$\displaystyle v = 1.7035~\frac{m}{s^2} \cdot 3.426~\boxed{s\approx 5.837~\frac{m}{s}}$