Bullet in a block hitting a spring

[preluderacer]

Homework Statement

An 8-g bullet is shot into a 4.0-kg block, at rest on a frictionless horizontal surface. The bullet remains lodged in the block. The block moves into a spring and compresses it by 5.0 cm. The force constant of the spring is 2200 N/m. In the figure, the initial velocity of the bullet is closest to:

The Attempt at a Solution

what I did was set (mbullet+mblock)vblock=1/2(k)x^2 I solved the the velocity of the block and got 0.686 m/s. Then I set mbullet(v)bullet=(m1+m2)vblock and solved for the vbullet and got 343N. This answer doesn't seem quite right. What am I doing wrong?

 

[ehild]

what I did was set (mbullet+mblock)vblock=1/2(k)x^2 I solved the the velocity of the block and got 0.686 m/s.

The left-hand side of your equation is momentum, the right-hand side is energy. They can not be equal.

ehild

 

[preluderacer]

i think i got it 1/2(m+M)v^2=1/2(k)(x)^2

 

[ehild]

Write out the kinetic energy of the block with the bullet inside. ehild

 

[rwisz]

I would first check the units used in the calculation. It seems like there may be a mix-up of units, as the velocity of the bullet is given in Newtons (a unit of force) rather than meters per second (a unit of velocity). It is important to use consistent units in calculations to avoid errors.

Additionally, I would also check the equations and variables used in the calculation. It is important to use the correct equations and plug in the correct variables to get an accurate answer. In this case, the equation used should be conservation of momentum, rather than the equation for work and energy.

I would also double check the given values and make sure they are accurate and consistent. Sometimes, small errors in input values can lead to significant differences in the final answer.

Lastly, I would recommend checking the overall approach to the problem. Are all the necessary variables and factors being considered? Is there any assumption being made that may not be valid? It is always important to critically evaluate the approach to a problem to ensure accuracy.