Air track
8
2.
Uniformly accelerated rectilinear motion
-
Equip the track with the pulley holder (see §3.2) and the glider with
the hook accessory (0.8g).
-
Fasten the string to the glider and place a hooked weight (mass M) at
the other end (passing the thread over the pulley).
-
Release the glider using the launcher (without a spring).
-
Place the photogates x mm apart and measure the glider's travel time
between the 2 photogates.
-
Repeat the operation 3 times moving the 2 photogates X mm further
along the track (keeping the x mm gap between them).
-
This demonstrates that the travel time increases along the track.
The velocity increases constantly.
The acceleration is constant.
𝑣 =
𝑡
𝑐ℎ𝑟𝑜𝑛𝑜
𝑥
𝑎⃗ =
𝑣
2
⃗⃗⃗⃗⃗ − 𝑣
1
⃗⃗⃗⃗⃗
𝑡
2
− 𝑡
1
=
𝑣
3
⃗⃗⃗⃗⃗ − 𝑣
2
⃗⃗⃗⃗⃗
𝑡
3
− 𝑡
2
-
In addition, the force exerted on the glider is:
𝑇
𝑐
⃗⃗⃗⃗ = 𝑚
𝑐
∗ 𝑎
𝑐
⃗⃗⃗⃗⃗
-
If we balance the forces at the weighted mass, this gives:
𝑀 ∗ 𝑔⃗ + 𝑇
𝑚
⃗⃗⃗⃗⃗⃗ = 𝑀 ∗ 𝑎
𝑚
⃗⃗⃗⃗⃗⃗
With
𝑔
⃗⃗⃗⃗
and
𝑇
𝑚
⃗⃗⃗⃗⃗⃗
with opposite directions
-
Now
𝑇
𝑐
⃗⃗⃗⃗ = −𝑇
𝑚
⃗⃗⃗⃗⃗⃗
and as the acceleration of the glider is the same as that
of the mass,
𝑎 =
𝑀∗𝑔
𝑀+𝑚
𝑐
