Question

В лежащий на длинном столе деревянный брусок массой M попадает летящая горизонтально со скоростью V пуля массой m и застревает в нём. Сколько времени после этого брусок будет скользить по столу, если коэффициент трения между столом и бруском равен μ?

Answer 1

Δv=v
m*Δv=F*Δt
F=μ*N=μ*(M+m)*g
Δt=m*v/(μ*(M+m)*g)
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Answer 2

Calculation of the Time the Block Slides on the Table

To calculate the time it takes for the block to slide on the table after the bullet gets embedded in it, we need to consider the conservation of momentum and the forces acting on the block.

Let's denote the mass of the block as M and the mass of the bullet as m. The initial velocity of the bullet is V, and the coefficient of friction between the block and the table is μ.

According to the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Since the bullet gets embedded in the block, the final velocity of the block-bullet system will be the same as the initial velocity of the bullet.

The momentum before the collision is given by the product of the mass and velocity of the bullet:

mV.

The momentum after the collision is given by the product of the mass of the block-bullet system and its final velocity:

(M + m)V_f.

Setting these two equal, we have:

mV = (M + m)V_f.

Simplifying, we find:

V_f = (mV) / (M + m).

Now, let's consider the forces acting on the block as it slides on the table. The force of friction opposing the motion is given by:

F_friction = μ * (M + m) * g,

where g is the acceleration due to gravity.

The acceleration of the block-bullet system is given by:

a = F_friction / (M + m).

The time it takes for the block to slide a certain distance can be calculated using the equation of motion:

s = ut + (1/2)at^2,

where s is the distance traveled, u is the initial velocity, a is the acceleration, and t is the time.

In this case, the distance traveled is the length of the table, and the initial velocity is zero since the block starts from rest. Rearranging the equation, we get:

t = sqrt((2s) / a).

Substituting the values, we can calculate the time it takes for the block to slide on the table.

Please provide the values of M, m, V, and μ so that we can proceed with the calculation.