Calculating Coefficient of Friction and Kinetic Energy in Bullet-Block Collision

In summary, A bullet with a velocity of 400 m/s passes through a wooden block of mass 0.800 kg, causing the block to slide 45 cm along a surface. The bullet's speed decreases to 120 m/s. The coefficient of kinetic friction between the block and surface is 0.222. The decrease in kinetic energy of the bullet is -291J, and the kinetic energy of the block at the instant after the bullet passes through it is 0.784 J. To solve this problem, conservation of momentum and energy were applied, and the work done by friction was equal to the change in kinetic energy of the system. The mass of the bullet is 0.004 kg. The block's velocity after
  • #1
marialo
12
0
I'm having trouble with this physics problem:

A bullet traveling horizontally with a velocity of magnitude 400 m/s, is fired into wooden block with mass 0.800 kg initially at rest on a level surface. The bullet passes through the block and emerges with its speed reduced to 120 m/s. the block slides a distance of 45 cm along the surface from its initial position. A) what is the coefficient of kinetic friction between the block and surface? B) what is the decrease in kinetic energy of the bullet? C) what is the kinetic energy of the block at the instant after the bullet passes through it?

i started doing part A, and found that the velocity while the bullet is in the block is 1.99 m/s. i also assumed that the work done by friction was equal to the change in kinetic energy of the system. but when i used this information to solve for the coefficient of friction i got something way too high. the answers are supposed to be : A) 0.222, B)-291J, C)0.784 J, but i have no idea of how to set this problem up. Please Help!
 
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  • #2
What's the mass of the bullet?
 
  • #3
Doc Al said:
What's the mass of the bullet?

Sorry, i forgot to metion that the bullet is 4.0 g, or 0.004 kg
 
  • #4
First thing to do: Find the speed of the block immediately after the bullet passes through it, before it starts its slide along the surface. (Hint: Apply conservation of momentum.)
 
  • #5
did you try to split up original KE of bullet
between bullet and block?
(1.99 m/s too high for block)
 
  • #6
Doc Al said:
First thing to do: Find the speed of the block immediately after the bullet passes through it, before it starts its slide along the surface. (Hint: Apply conservation of momentum.)

i already did that. since momentum is conserved, the momentum of the bullet initially is equal to the sum of the momentums after the collision. i found that the velocity off the block after collision was 1.4 m/s.
 
  • #7
knowing the block's KE after bullet passes,
and Work done by friction (formula),
what's the Friction *Force*?
 
  • #8
The work done be friction is d*mg(mu), where mg(mu) is the force of friction. the block's KE is just 1/2mv^2, right?
 
  • #9
Now that you have the speed of the block, use kinematics to find the acceleration and required friction force.
 
  • #10
yea, KE known, mu is straightforward.

Because LOCATIONS were known/wanted,
this was best solved using an Energy approach.
If you had been given/asked about TIMES,
momentum (or F=ma) would've been best.

(notice you answered "C" first).

(Why is the Change of bullet KE NOT = KE block?)
 
Last edited:
  • #11
Sorry, I'm still having trouble seeing how to go from KE to mu
 
  • #12
umm, the KE of the block is removed by the
(negative) Work that the friction Force does on the block.

You got the block's KE before sliding, right?
(Where does that KE go AS it SLIDES?)
 
  • #13
Alright, so velocity of the block is 1.4 m/s as marialo stated and I also found.
so since KE is the only thing that changes, KE=Work of Friction.
Work of friction = (8mu)(.45)(-1) = -3.6mu
KE = (.8/2)(1.4)^2=.784
mu = .217777...
Why didn't I get .222 as the book states to be the answer? Did I do anything wrong or it's a negligible error?
 

1. What is Bullet Block Collision?

Bullet Block Collision is a phenomenon that occurs when a fast-moving projectile (or bullet) hits a stationary or moving object (or block). It is a common concept in physics and is often studied in the field of mechanics.

2. What factors affect Bullet Block Collision?

The factors that affect Bullet Block Collision include the velocity and mass of the bullet, the density and material of the block, and the angle and surface area of impact. These factors determine the amount of force and energy transferred during the collision.

3. How is Bullet Block Collision calculated or measured?

Bullet Block Collision can be calculated or measured using the principles of conservation of momentum and energy. By analyzing the velocity and mass of the bullet and block before and after the collision, the resulting force and energy can be determined.

4. What are the real-world applications of Bullet Block Collision?

Bullet Block Collision has various real-world applications, including in ballistics and firearms, car collisions and safety, and sports such as billiards and golf. Understanding the mechanics of Bullet Block Collision can also help engineers design stronger and more durable structures.

5. How can Bullet Block Collision be used to improve safety?

By studying Bullet Block Collision, scientists and engineers can develop safety measures and equipment to reduce the impact and damage from high-velocity collisions. This can include designing better helmets or body armor, creating safer car designs, and improving building construction to withstand strong impacts.

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