amandab727
Answered

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55. A projectile of mass 2.0 kg is fired in the air at an angle of 40.0° to the horizon at a speed of 50.0 m/s. At
the highest point in its flight, the projectile breaks into three parts of mass 1.0 kg, 0.7 kg, and 0.3 kg. The 1.0-
kg part falls straight down after breakup with an initial speed of 10.0 m/s, the 0.7-kg part moves in the original
forward direction, and the 0.3-kg part goes straight up.
At peak after explosion
V3,f = (V3,1))
At peak before explosion
V₁
=
(V₁.x)x
m3 = 0.3 kg
m₂ = 0.7 kg
V2,1 = (v₂,1)
m₁ = 1.0 kg
V₁ = (50.0 m/s)v₁
₁,f= -(10.0 m/s)
40°
Launch
a. Find the speeds of the 0.3-kg and 0.7-kg pieces immediately after the break-up.
b. How high from the break-up point does the 0.3-kg piece go before coming to rest?
c. Where does the 0.7-kg piece land relative to where it was fired from?

Sagot :

marianaegarciaperedo

The total moment in an islated system remains constant through time. a) V₂ = 109.43 m/s and V₃ = 33.33 m/s. b) h = 56.67 m. c) d = 480 m.

What is the law of conservation of momentum?

First let us remember that momentum or lineal momentum is a motion quantity. In physics it is the fundamental quantity that characterizes the motion of any object.

The momentum is a vectorial quantity that can be calculated as the product of the object mass by its lineal velocity ⇒ mv

The total lineal moment of a system constituted by a group of objects is the sum of the vectorial moments of each of the objects.

In an isolated system -the one that does not interact with the exterior environment-, the moment remains constant through time. This is the law of conservation of momentum. The initial moment is equal to the final moment ⇒ Pinitial = Pfinal

Objects involved in crushes, explosions, collitions, and others, are considered to be isolated systems.  

.......................

So, in the exposed example we know that,

  • Projectile mass ⇒2kg.
  • Velocity = 50 m/s.
  • Angle⇒ 40°.
  • Smaller masses ⇒ 1 kg with 10m/s speed, 0.7 kg, and 0.3 kg.

a) We need to calculate the speed of the 0.7 and 0.3 kg objects.

So, 0.7 kg object moves in the original forward direction, meaning that we can use the following formula to calculate its velocity,

m₀v₀ = m₂v₂

Where

  • m₀ = projectile mass = 2kg
  • v₀ = horizontal component of projectile velocity
  • m₂ = object mass = 0.7 kg
  • v₂ = object velocity = ??

So first, we need to get the horizontal component of projectile velocity, V₀.

V₀ = V cosθ

V₀ = 50 cos40º

V₀ = 38.3 m/s

Now we can calculate the velocity of the 0.7 kg object.

m₀v₀ = m₂v₂

2 kg x 38.3 m/s = 0.7 kg x v₂

v₂ = (2 x 38.3) / 0.7

v₂ = 109.43 m/s

Now we need to calculate the velocity of the 0.3 kg object. Since this part goes exactly in the opposite direction of the 10 kg object, their addition will equal zero. So we can use the following equation to calculate the velocity of the 0.3 kg object.

m₁v₁ + m₃v₃ = 0

Where

  • m₁ = 1 kg object mass
  • v₁ = 1 kg object velocity = 10m/s
  • m₃ = 0.3 kg object mass
  • v₃ = object velocity = ??

m₁v₁ + m₃v₃ = 0

(1 kg x 10m/s) + (0.3 kg x v₃ ) = 0

(0.3 kg x v₃ ) = - (1 kg x 10m/s)

v₃ = - (1 kg x 10m/s) / 0.3

v₃ = - 33.33 m/s

The - sign is indicating the opposite direction concerning the 1 kg object.

ANSWER:

  • The speed of the 0.7 kg object is 109.43 m/s
  • The speed of the 0.3 kg objects is 33.33 m/s

.........................

b) We need to get the high from the break-up point where the 0.3-kg piece go before rest

At rest,

1/2 m₃v₃² = m₃gh

Where,

  • m₃ = 0.3 kg object mass
  • v₃ = object velocity = 33.33m/s
  • g = gravity = 9.8 m/s²
  • h = high = ??

1/2 m₃v₃² = m₃gh

h = 1/2 (v₃²) /g

h = 1/2 (33.33²) / 9.8

h = 56.67 m

ANSWER: The high from the break-up point where the 0.3-kg piece go before coming to rest is 56.67 m.

........................

c) Finally, we need to get where does the 0.7-kg piece land

ANSWER: The distance at which the 0.7 piece lands, concerning the point from which it was fired is 480 m.

You can learn more about law of conservation of momentum at

https://brainly.com/question/17140635

https://brainly.com/question/1113396

#SPJ1

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