Understanding the Forces
* Gravity: The main force acting on the mass is gravity, pulling it straight down (towards the center of the Earth). This force is constant, regardless of the angle you hold the mass.
* Your Force: You exert a force upward to counteract gravity and keep the mass from falling. This is the force we're interested in.
The Role of Angle
The angle at which you hold the mass determines how much of your force needs to directly oppose gravity.
* Smaller Angle (10 degrees): When the angle is small, most of your force is acting directly upward, opposing the force of gravity. You're essentially lifting almost the entire weight of the mass.
* Larger Angle (70 degrees): When the angle is larger, your force has a horizontal component in addition to the vertical component. The horizontal component does not directly oppose gravity, making your vertical force smaller. You're essentially supporting a smaller fraction of the mass's weight.
Trigonometry to the Rescue
You can use trigonometry to calculate the exact force you need to exert at different angles:
* Vertical Component: The vertical component of your force is calculated as `F * cos(theta)`, where F is the total force you exert and theta is the angle.
* Horizontal Component: The horizontal component is calculated as `F * sin(theta)`.
Conclusion
The smaller the angle, the more your force is directly opposing gravity, and the greater the force you need to exert. Conversely, at a larger angle, a smaller fraction of your force is opposing gravity, requiring less effort from you.
