Energy? Momentum? Collision?

In summary, the 34g bullet traveling at 120m/s embeds itself in a wooden block which then collides with a spring with a spring constant of 99N/m. The block compresses the spring a maximum of 1.2 cm. Using the equations m1v1 + m2v2 = (m1 + m2)v' and Ee = .5kx2, the mass of the wooden block can be calculated to be reasonably large due to the small compression of the spring.
  • #1
blindsided
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Homework Statement


A 34g bullet traveling at 120m/s embeds itself in a wooden block on a smooth surface. The block then slides toward a spring and collides with it. The block compresses the spring (k=99N/m) a maximum of 1.2 cm. Calculate the mass of the block of wood.


Homework Equations


Not sure.
m1v1 + m2v2 = (m1 + m2)v'
Ee = .5kx2
Ek = .5mv2


The Attempt at a Solution


I'm fairly certain it's incorrect. I just don't know where.
IMG_NEW.jpg


Thanks!
 
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  • #2
I see your concern with the mass of the wooden block. Your approach is correct. Consider the spring. It has a spring constant of 99N/m. This means if the spring were used as a scale a 10 kg mass would compress the spring 1 meter. A very weak spring. Since the spring compressed .012 meters your answer is reasonable; the velocity of the bullet-block system would have to be very small meaning a very large mass for the block.
 
  • #3


I would approach this problem by first identifying the relevant quantities and their relationships. In this case, we are dealing with energy, momentum, and collisions.

Energy is a fundamental concept in physics that describes the ability of a system to do work. In this scenario, the bullet has kinetic energy due to its motion, which is converted into potential energy as it compresses the spring. The formula for calculating the potential energy of a spring is Ee = 0.5kx^2, where k is the spring constant and x is the displacement of the spring.

Momentum is a conserved quantity in collisions, meaning that the total momentum of the system before and after the collision remains constant. In this case, we can use the equation m1v1 + m2v2 = (m1 + m2)v' to calculate the momentum of the system before and after the collision, where m1 and v1 are the mass and velocity of the bullet, m2 and v2 are the mass and velocity of the block, and v' is the final velocity of the combined system.

In order to solve for the mass of the block, we can use the equation for kinetic energy, Ek = 0.5mv^2, where m is the mass of the block and v is its final velocity after the collision with the spring. We can set this equal to the potential energy of the spring, Ee, and solve for the mass of the block.

Overall, it is important to carefully consider the relevant equations and the relationships between the different quantities in order to arrive at a correct solution. It may also be helpful to draw a diagram and label all known quantities in order to visualize the problem better.
 

1. What is energy?

Energy is the ability to do work. It is a fundamental property of matter and can exist in many forms, such as kinetic, potential, thermal, chemical, and nuclear. Energy is also conserved, meaning it cannot be created or destroyed, only transformed from one form to another.

2. How is momentum defined?

Momentum is a measure of an object's motion and is defined as the product of its mass and velocity. In other words, momentum = mass x velocity. It is a vector quantity, meaning it has both magnitude and direction, and is conserved in a closed system.

3. What happens during a collision?

During a collision, two or more objects come into contact with each other and exert forces on each other for a short period of time. This can result in a transfer of energy and momentum between the objects. In an elastic collision, kinetic energy and momentum are conserved, while in an inelastic collision, some of the kinetic energy is converted into other forms, such as heat or sound.

4. How is energy related to momentum?

Energy and momentum are related through the principle of conservation of energy. In a closed system, when there is no external forces acting on the objects, the total energy and momentum will remain constant. This means that if one object gains momentum, another object must lose an equal amount of momentum in the opposite direction to maintain the total momentum of the system.

5. Why is the concept of energy important?

The concept of energy is important because it is a fundamental aspect of the universe and is involved in virtually every physical process and phenomenon. It allows us to understand and predict the behavior of objects, from the smallest particles to the largest galaxies. Energy is also essential for our daily lives, as it is the source of power for our homes, transportation, and technology.

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