Question

Assume: The bullet penetrates into the block and stops due to its friction with the block. The compound system of the block plus the bullet rises to a height of 10 cm along a circular arc with a 18 cm radius.
Assume: The entire track is frictionless. A bullet with a m1 = 30 g mass is fired horizontally into a block of wood with m2 =
4.8 kg mass.
The acceleration of gravity is 9.8 m/s^2.
Calculate the total energy of the composite system at any time after the collision. Answer in units of J.
Taking the same parameter values as those in Part 1, determine the initial velocity of the bullet. Answer in units of m/s.

Answer 1

Answer:

1)4.7334J

2)225.4m/s

Explanation:

v= the Velocity of both the bullet and the block after collision=?

H= Height of the bullet along circular arc= 10cm=0.1m

g= acceleration due to gravity= 9.81m/s^2

R= Radius of the circular arc= 18cm= 0.18m

m= Mass of the bullet= 30g= 0.03kg

M= Mass of the block = 4.8 kg

Using the law of conservation of energy

Potential energy of the system= Kinectic energy of the system

1/2 mv^2= mgh..............eqn(1)

But we have two mass m and M

We can write eqn(1) as

0.5(m+M)v^2= (m+M)gh ...........eqn(2)

If we make "v" subject of the formula we have

v = √2gh

Then substitute the values we have

= √2 x 9.81 x 0.1 = 1.40m/s

1) We can now calculate the total energy of the system after collision as

KE = 1/2(m+M)v^2

= 1/2 x (0.03+4.8) x (1.40)^2

KE = 4.7334J

Hence, the total energy of the composite system at any time after the collision is 4.7334J

2)to determine the initial velocity of the bullet.

From law of momentum conservation, which can be expressed as

m1u1+m2u2=(m1+m2)v

Where the initial Velocity of the bullet u1= ?

Final velocity of the bullet = 0

the Velocity of both the bullet and the block after collision=v= 1.40m/s

(0.03×u1) +(u×0)= (4.8+0.03)1.4

0.03u1=6.762

U1=225.4m/s

Hence, the initial velocity of the bullet is 225.4m/s

Answer 2

The total energy of the composite system at any time after the collision is 4.7334 J and initial velocity of the bullet is 225.4 m/s.1`

What is conservation of momentum?

Momentum of a object is the force of speed of it in motion. Momentum of a moving body is the product of mass times velocity.

When the two objects collides, then the initial collision of the two body is equal to the final collision of two bodies by the law of conservation of momentum.

• Total energy of the composite system at any time after the collision-

The mass of the bullet is 30g and the mass of the wood block is 4.8 kg. Thus the total mass of these two is,

$m=0.03+4.8\\m=4.83 \rm kg$

As the compound system of the block plus the bullet rises to a height of 10 cm. Thus, the speed of it is,

$v=\sqrt{2gh}\\v=\sqrt{2\times9.81\times0.1}\\v=1.4\rm m/s$

Now, the total energy of the composite system at any time after the collision is equal to the kinetic energy. Therefore,

$E=\dfrac{1}{2}mv^2\\E=\dfrac{1}{2}4.83(1.4)^2\\E=4.7334\rm J$

Total energy of the composite system at any time after the collision is 4.7334 J.

• The initial velocity of the bullet-

The block was at rest initial, thus it has initial velocity of it is zero. Thus, the initial momentum of the bullet is equal to the final momentum of bullet and block. Therefore,

$0.03\times u_o=4.83\times1.4\\u_o=225.4\rm m/s$

Thus, the total energy of the composite system at any time after the collision is 4.7334 J and initial velocity of the bullet is 225.4 m/s.1`

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