The ratio between two horizontal speeds in this pendulum arrangement

Thread starter billtodd
Start date Mar 27, 2024
Tags

equations Horizontal Torque

In summary, the study examines the relationship between two horizontal speeds within a pendulum system, focusing on how these speeds interact under various conditions. It highlights the mathematical and physical principles governing the movement, ultimately providing insights into the dynamics involved in the arrangement.

Mar 27, 2024

billtodd

Homework Statement: To find the ratio between the horizontal speed of the stick with mass ##M## and the small point with mass ##m##.

Relevant Equations: Force equation and torque.

From the forces equation I can only understand from it that the forces' equations are:##N=Mg## and ##T\sin \theta=m\ell \ddot{\theta}##.

But I don't know how to find the Torques' equations.

Any help is appreciated.

N=Mg ##Tcos⁡θ+N=mg

Physics news on Phys.org

Mar 27, 2024

berkeman

Mentor

Could you please type out the text from your attachment, and explain that setup? Thanks.

FAQ: The ratio between two horizontal speeds in this pendulum arrangement

What is the ratio between two horizontal speeds in a pendulum arrangement?

The ratio between two horizontal speeds in a pendulum arrangement depends on the specific points in the pendulum's swing you are comparing. Generally, the speed is highest at the lowest point of the swing (equilibrium position) and decreases as the pendulum moves towards the endpoints (maximum displacement). The ratio can be calculated using principles of conservation of energy.

How do you calculate the horizontal speed of a pendulum?

The horizontal speed of a pendulum can be calculated using the equation \( v = \sqrt{2gh} \), where \( v \) is the speed, \( g \) is the acceleration due to gravity, and \( h \) is the height difference from the lowest point. For horizontal speed specifically, you can project this speed onto the horizontal axis considering the angle of displacement.

What factors affect the horizontal speed ratio in a pendulum?

The horizontal speed ratio in a pendulum is affected by the length of the pendulum, the angle of displacement, and gravitational acceleration. Air resistance and friction at the pivot point can also play a role in real-world scenarios, although they are often negligible in idealized models.

Can the horizontal speed ratio be greater than 1 in a pendulum arrangement?

No, the horizontal speed ratio cannot be greater than 1 when comparing the same pendulum at different points in its swing. The speed is always highest at the equilibrium position and decreases towards the endpoints, so the ratio of speed at any point to the maximum speed (at the bottom) will always be less than or equal to 1.

How does the angle of displacement influence the horizontal speed ratio?

The angle of displacement influences the horizontal speed ratio because it determines the height difference from the lowest point of the swing. A larger angle of displacement means a greater height difference and thus a higher potential energy at the endpoints, which translates into a greater variation in speed as the pendulum swings. The horizontal component of the speed will vary accordingly with the cosine of the angle of displacement.