1) a bullet of mass 0.02 kg is fired into a block of wood of mass 1.5 kg resting on a horizontal table. The block moves offwith an initial speed of 8 m/s. Estimate the speed with the bullet strikes the block.

2) The bullet in question 1 is fired from a rifle of mass 2.5 kg. Assuming that the bullet leaves the barrel of the rifle with the speed calculated above, find the recoil speed of the rifle if it is free to move. In reality the rifle is held and for a certain person the rifle recoils a distance of 0.12 m. Determine the average force that the person exerts on the rifle?

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To answer both questions, we will be applying the concepts of conservation of momentum and the principle of conservation of energy.

1) To estimate the speed at which the bullet strikes the block, we will use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision in a closed system.

The momentum of an object is calculated by multiplying its mass by its velocity. Let's assume the initial velocity of the bullet is v (which we need to find) and the final velocity of the bullet and block together is V.

The initial momentum of the bullet is given by p₁ = m₁ * v, where m₁ is the mass of the bullet and v is the initial velocity of the bullet.

The initial momentum of the block is given by p₂ = m₂ * 0 (since the block is initially at rest), where m₂ is the mass of the block.

The total initial momentum p₁ + p₂ is equal to the total final momentum. Therefore, m₁ * v = (m₁ + m₂) * V.

Given that the mass of the bullet (m₁) is 0.02 kg, the mass of the block (m₂) is 1.5 kg, and the initial speed of the block (V) is 8 m/s, we can solve for the velocity of the bullet (v).

v = (m₁ + m₂) * V / m₁
v = (0.02 + 1.5) * 8 / 0.02
v ≈ 616 m/s

Therefore, the estimated speed at which the bullet strikes the block is approximately 616 m/s.

2) To find the recoil speed of the rifle, we can again apply the principle of conservation of momentum. The total momentum before the bullet is fired is equal to the total momentum after the bullet is fired.

Let's assume the initial velocity of the rifle is Vᵣ and the final velocity of the rifle after the bullet is fired is vᵣ.

The initial momentum of the rifle is given by Pᵣ = Mᵣ * Vᵣ, where Mᵣ is the mass of the rifle and Vᵣ is the initial velocity of the rifle.

The initial momentum of the bullet is given by p₁ = m₁ * v, where m₁ is the mass of the bullet (0.02 kg) and v is the velocity of the bullet (which we calculated in the first question, approximately 616 m/s).

The total initial momentum Pᵣ + p₁ is equal to the total final momentum, which is given by Mᵣ * vᵣ.

Therefore, Mᵣ * Vᵣ + m₁ * v = Mᵣ * vᵣ.

Given that the mass of the rifle (Mᵣ) is 2.5 kg and the mass of the bullet (m₁) is 0.02 kg, and using the previously calculated velocity of the bullet (v ≈ 616 m/s), we can solve for the recoil velocity of the rifle (vᵣ).

vᵣ = (Mᵣ * Vᵣ + m₁ * v) / Mᵣ
vᵣ = (2.5 * 0 + 0.02 * 616) / 2.5
vᵣ ≈ 0.4928 m/s

Therefore, the estimated recoil speed of the rifle is approximately 0.4928 m/s.

To determine the average force exerted by the person holding the rifle, we can use the impulse-momentum principle, which states that the change in momentum of an object is equal to the impulse applied to it.

The impulse (J) applied to the rifle can be calculated by multiplying the average force (F) exerted over a certain time interval (Δt).

J = F * Δt

The impulse J is equal to the change in momentum Δp of the rifle. Since the rifle starts from rest and ends up with a recoil velocity of vᵣ, the impulse applied to the rifle is equal to the momentum of the rifle.

J = Δp = Mᵣ * vᵣ

Therefore, the average force exerted by the person holding the rifle can be calculated as:

F = J / Δt = (Mᵣ * vᵣ) / Δt

Given that the rifle recoils a distance of 0.12 m, we can determine the time interval (Δt) using the equation of motion: Δt = Δx / vᵣ, where Δx is the distance traveled by the rifle (0.12 m) and vᵣ is the recoil velocity of the rifle.

Δt = 0.12 / vᵣ
Δt = 0.12 / 0.4928
Δt ≈ 0.2431 s

Now we can calculate the average force exerted by the person:

F = (Mᵣ * vᵣ) / Δt
F = (2.5 * 0.4928) / 0.2431
F ≈ 5.0979 N

Therefore, the average force exerted by the person holding the rifle is approximately 5.0979 Newtons.