What is the Angle of Deflection in a Colliding Ball and BB Gun Problem?

In summary, the problem involves a rubber ball being shot with a BB gun in an attempt to win a prize. The mass of the ball and BB are given, as well as the muzzle speed of the gun. The angle of deflection refers to the angle the string makes with the vertical. The solution involves solving for the velocity of the combined bullet/ball and using that to calculate the angle through trigonometry.
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Homework Statement



A 280 g rubber ball is hanging from a 27cm long swing in a booth at a carnival. A little girl shoots it with a BB gun in attempt to win a gigantic, stuffed Daffy Duck doll. The mass of each BB is 3g and the muzzle speed of the gun is 21m/s. If the BB penetrates the ball (and gets stuck inside), what is the mass angle of deflection of the ball?

Homework Equations



p=mv (momentum), conservation of momentum, trigonometry.

The Attempt at a Solution



I feel confident that I could solve this using some trig and momentum if I knew what the problem meant-what is an angle of deflection? If it's what I think it is (at what angle they collide) then could there be one if the two are stuck together? Or is it the angle through which the ball swings? Any ideas?
 
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  • #2
Welcome to PF.

The angle of deflection is the angle the string makes with the vertical.

Solve for the velocity of the combined bullet/ball first. Then use that velocity as the kinetic energy that gets consumed by gravity as it swings upward. KE after impact will of course equal the potential energy PE at its height.

Using that height and an appropriate trig function you should be able to solve directly for the angle.
 
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  • #3
Thanks so much, I understand now.
 

FAQ: What is the Angle of Deflection in a Colliding Ball and BB Gun Problem?

What is the Angle of Deflection problem?

The Angle of Deflection problem is a physical phenomenon that occurs when a beam or structure is subjected to a force, causing it to bend or deform. It is a common problem in engineering and mechanics, and it is important to understand the factors that affect the amount of deflection in order to design structures that can withstand these forces.

What are the factors that affect the Angle of Deflection?

The Angle of Deflection is affected by several factors, including the magnitude and direction of the applied force, the material properties of the structure, and the shape and dimensions of the structure. The type and distribution of the load also play a significant role in determining the amount of deflection.

How is the Angle of Deflection calculated?

The Angle of Deflection can be calculated using various mathematical equations and principles, depending on the type of structure and the type of load. For simple cases, the deflection can be calculated using equations such as the Euler-Bernoulli beam theory or the Timoshenko beam theory. For more complex cases, finite element analysis is often used to calculate the deflection.

What are the practical applications of understanding the Angle of Deflection?

Understanding the Angle of Deflection is crucial in the design and analysis of structures such as bridges, buildings, and machines. It allows engineers to predict the amount of deflection that a structure will experience under different loading conditions, and to design structures that can safely withstand these forces without failing or collapsing.

How can the Angle of Deflection be minimized?

There are several ways to minimize the Angle of Deflection in a structure, including using materials with higher stiffness and strength, increasing the cross-sectional area of the structure, and adding additional support or reinforcement. It is also important to carefully consider the type and distribution of the load in order to minimize the deflection.

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