Find Max Speed for Smaller Mass in Trebuchet w/ Stiff Rod & 2 Masses

[semc]

Imagine a trebuchet with a stiff rod of 3m and neligible mass.Two masses 60kg and 0.12kg are at its end with the bigger mass 0.14m away from the pivot point. Find the maximum speed the smaller mass attain.

Actually i posted this before but it seems i can't get the answer provided in the book. So what i did was to assume the initial position of the masses to be at 0 potential so initially they have no energy. Then i consider the case when the rod is vertical which gives me the equation - MgL+ [tex]\frac{1}{2}[/tex]Mv₁² - mg(0.14) = 0. In this case i assume the bigger mass to stop moving when it reaches the bottom. Am i allowed to make this assumption? If not how do i calculate for the velocity of the bigger mass?

Since the smaller mass is significantly smaller than the bigger mass, i use mg(0.14) - [tex]\frac{1}{2}[/tex]mv₂²=0 to estimate the velocity of the bigger mass and find the angular velocity from there. I use v=r[tex]\omega[/tex] to calculate the velocity of the smaller mass however the answer i got was way too smaller compared to the answer why is this so?

 

[Andrew Mason]

Imagine a trebuchet with a stiff rod of 3m and neligible mass.Two masses 60kg and 0.12kg are at its end with the bigger mass 0.14m away from the pivot point. Find the maximum speed the smaller mass attain.

Actually i posted this before but it seems i can't get the answer provided in the book. So what i did was to assume the initial position of the masses to be at 0 potential so initially they have no energy. Then i consider the case when the rod is vertical which gives me the equation - MgL+ [tex]\frac{1}{2}[/tex]Mv₁² - mg(0.14) = 0. In this case i assume the bigger mass to stop moving when it reaches the bottom. Am i allowed to make this assumption? If not how do i calculate for the velocity of the bigger mass?

Since the smaller mass is significantly smaller than the bigger mass, i use mg(0.14) - [tex]\frac{1}{2}[/tex]mv₂²=0 to estimate the velocity of the bigger mass and find the angular velocity from there. I use v=r[tex]\omega[/tex] to calculate the velocity of the smaller mass however the answer i got was way too smaller compared to the answer why is this so?

You are not taking the correct approach. You have to analyse the problem from the point of view of energy.

The energy of the falling large mass does three things. The loss of potential energy of the large mass gives the large mass kinetic energy; it gives the smaller mass kinetic energy; and it does something else that uses energy. (hint: What happens to the potential energy of the small mass as the large mass falls?). The large mass does not stop when it reaches the bottom. It oscillates until it gradually stops.

When you determine how much energy is kinetic energy, you can determine the speeds. What is the relationship between the tangential speeds of the masses?

AM

 

[tomcue]

I would say that your approach to solving this problem is reasonable, but there are a few things to consider.

First, it is important to clarify what is meant by "maximum speed" for the smaller mass. Are we looking for the maximum linear speed, or the maximum angular speed? These may not be the same, as the motion of the masses in the trebuchet involves both linear and rotational motion.

Second, your assumption that the bigger mass stops moving when it reaches the bottom may not be entirely accurate. In reality, there will be some energy loss due to friction and air resistance, so the bigger mass may not come to a complete stop. Additionally, the motion of the smaller mass will also affect the motion of the bigger mass, so it may not be a simple case of one mass stopping and the other continuing to move.

To accurately calculate the maximum speed of the smaller mass, you will need to consider the motion of both masses and the conservation of energy and momentum in the system. This will require solving a system of equations, which may be more complex than the equations you have used.

As for the discrepancy between your calculated velocity and the answer in the book, it is possible that there is an error in your calculations or assumptions. It would be helpful to double-check your work and make sure all the variables and equations are correct.

In summary, while your approach is a good starting point, it may not be sufficient to accurately determine the maximum speed of the smaller mass in this trebuchet system. Further analysis and consideration of all factors involved will be necessary for a more accurate calculation.