Energy released during explosion

In summary, a projectile of mass 20.6 kg is fired at an angle of 59.0^\circ above the horizontal and with a speed of 76.0 m/s. At the highest point of its trajectory, the projectile explodes into two fragments with equal mass. One of the fragments falls vertically with zero initial speed. Using conservation of momentum and the kinetic energy equation, the speed of the top fragment was found to be 152 m/s. However, upon further calculations, it was discovered that the initial velocity of the projectile at the highest point was actually 39.14 m/s. After correcting this mistake, the correct answer of 59492.8 J was obtained for the energy released during the explosion.
  • #1
enter260
8
0
A projectile of mass 20.6 kg is fired at an angle of 59.0^\circ above the horizontal and with a speed of 76.0 m/s. At the highest point of its trajectory the projectile explodes into two fragments with equal mass, one of which falls vertically with zero initial speed. You can ignore air resistance.

How much energy is released during the explosion?




Conservation of momentum and Kinetic Energy Equation



Change in KE=Kf-Ki

So. I used conservation of momentum to find that the speed of the top fragment is 152 m/s. I plug it into the kinetic energy equations but my answer is not accepted on my homework site. I plugged in...
Change in KE= (.5)(10.3)(152)^2-(.5)(20.6)(16)^2=59492.8 J which is wrong.
 
Physics news on Phys.org
  • #2
The velocities of 152 m/s and 16 m/s in your energy equation both look wrong.

How did you get those numbers?
 
  • #3
[tex]\frac{1}{2} m1 v^2 = Energy Released + \frac{1}{2} m2 v^2 [/tex]
 
  • #4
m1 and m2 are two the two masses...
 
  • #5
Yes that equation is OK. I was asking how you got the two velocities 152 and 16 to plug into the equation.
 
  • #6
Typo on my part. I wanted initial velocity to be 76 m/s (instead of 16).
76 was given, and 152 I obtained through the conservation of momentum equation.

(20.6 kg)(76 m/s)= (10.3 kg) (Velocity of fragment)
Solving that equation yielded 152 m/s.
Is something wrong about that?

Assuming that velocity is correct and I use your equation sidrox, wouldn't I still get 59492.8 J since the velocity of the other particle is zero?
 
  • #7
The projectile has a velocity of 76 m/s when it is launched. The explosion occurs when it is at its highest point.

You need to find the velocity at the highest point first.

Remember for a projectile the horizontal component of velocity is constant. At the highest point the vertical component of velocity is 0.

After that mistake, what you did is correct.

If the whole projectile has velocity V at the highest point, then the two parts will have velocities 0 and 2V. That is what you did, except you used V = 76 m/sec and that is the wrong value.
 
  • #8
Many thanks. I solved for it correctly and calculated that the speed as the highest point turns out to be 39.14. Then I just plugged it in and it worked. Thank you again.
 

What is energy released during an explosion?

The energy released during an explosion is the sudden and rapid release of stored energy in the form of heat, light, sound, and pressure. This energy is typically released when a chemical reaction or nuclear reaction takes place, causing a sudden expansion of gases and a rapid increase in temperature.

What causes an explosion?

An explosion is caused by a rapid and violent release of energy, typically due to a chemical reaction or nuclear reaction. This release of energy results in a sudden increase in pressure and the production of heat, light, and sound.

How is the energy released during an explosion measured?

The energy released during an explosion is typically measured in joules (J) or kilojoules (kJ). This measurement can be determined through various methods, including pressure gauges, temperature sensors, and calculations based on the mass of the explosive material.

What factors affect the amount of energy released during an explosion?

The amount of energy released during an explosion can be influenced by several factors, including the type and amount of explosive material, the confinement of the explosion, and the environment in which the explosion occurs. Other factors such as the shape and size of the explosive device can also impact the amount of energy released.

What are some real-world applications of energy released during explosions?

Explosions are used in various industries, such as mining, construction, and demolition, to break up materials or structures. Explosions are also used in military operations, such as weapons and ammunition, and in scientific research, such as in the development of propulsion systems and in studying the effects of explosions on materials and structures.

Similar threads

Replies
1
Views
488
  • Introductory Physics Homework Help
Replies
6
Views
922
  • Introductory Physics Homework Help
Replies
6
Views
937
  • Introductory Physics Homework Help
Replies
4
Views
368
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
1K
  • Introductory Physics Homework Help
Replies
20
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
4K
Back
Top