Using a vector diagram explain why it i easier to do chinups when your hands are 30cm apart instead of 90cm apart. (Assume the force that is excerted by your arms are the same in both cases
To determine why it is easier to do chin-ups when your hands are 30cm apart instead of 90cm apart, we can analyze the vector diagram.
First, let's understand the concept of a vector. A vector represents both magnitude (the size or strength) and direction. In the case of chin-ups, the relevant vector is the force exerted by your arms.
Now, let's consider a simplified vector diagram for both scenarios - hands 30cm apart and hands 90cm apart.
In the case of hands 30cm apart, when you pull up, the force exerted by each arm can be represented by two upward vectors, which we can call F1 and F2. These vectors are close together, indicating that the force is concentrated and directed vertically upwards.
```
F1
^
/
/
/
/
O__O
\
\
\
v
F2
```
Now, let's consider the scenario with hands 90cm apart. Here, the force exerted by each arm is also represented by vectors F1 and F2, but they are significantly more spread out.
```
F1
^
/
/
/
/
O__O
\
\
\
v
F2
```
Analyzing these diagrams, we notice that when the hands are 30cm apart, the forces F1 and F2 have a smaller moment arm, which is the perpendicular distance from the pivot point (fulcrum) to the vector representing the force. This smaller moment arm reduces the torque required to overcome the downward force of body weight, making it easier to perform chin-ups.
In contrast, when the hands are 90cm apart, the moment arm increases, as the vectors representing force are farther away from the fulcrum. This larger moment arm increases the torque required to resist body weight, making it harder to perform chin-ups.
Therefore, based on this analysis, it is easier to do chin-ups when your hands are 30cm apart compared to when they are 90cm apart, assuming the force exerted by your arms is the same in both cases.