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Chapter 7: Q72P (page 170)

A gun fires a bullet vertically into a 1.40-kg block of wood at rest on a thin horizontal sheet, Fig. 7鈥�44. If the bullet has a mass of 25.0 g and a speed of 230 m/s, how high will the block rise into the air after the bullet becomes embedded in it?

Short Answer

Expert verified

The height of the block, \(h = 0.83\;{\rm{m}}\).

Step by step solution

01

Conservation of momentum

In this case, the block or bullet moves vertically, an inelastic collision occurs, and momentum is conserved. Also, after the collision, the energy is conserved in the rising of the block and bullet.

02

Given data

Given data:

The mass of the block,\(m = 1.40\;{\rm{kg}}\).

The mass of the bullet,\(m' = 25\;{\rm{g}}\).

The speed of the bullet, \(v' = 230\;{\rm{m/s}}\).

03

Calculate the height of the block

The relation to calculate the height can be written as follows:

\(v' = \frac{{m + m'}}{m}\sqrt {2gh} \)

Here,\(g\)is the gravitational acceleration, and h is the required height.

Plugging values in the above equation,

\(\begin{array}{c}230\;{\rm{m/s}} = \left( {\frac{{1.40\;{\rm{kg}} + \left( {25\;{\rm{g}} \times \frac{{1\;{\rm{g}}}}{{1000\;{\rm{g}}}}} \right)}}{{1.40\;{\rm{kg}}}}} \right)\sqrt {2\left( {9.81\;{\rm{m/}}{{\rm{s}}^2}} \right)h} \\h = 0.83\;{\rm{m}}\end{array}\)

Thus, \(h = 0.83\;{\rm{m}}\) is the height risen by the block.

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Most popular questions from this chapter

(II) Calculate the force exerted on a rocket when the propelling gases are being expelled at a rate of 1300 kg/s with a speed of \(4.5 \times {10^4}\;{\rm{m/s}}\).

The distance between a carbon atom \(\left( {m = 12\;{\rm{u}}} \right)\) and an oxygen atom \(\left( {m = 16\;{\rm{u}}} \right)\) in the CO molecule is \({\bf{1}}{\bf{.13 \times 1}}{{\bf{0}}^{{\bf{10}}}}\;{\bf{m}}\) How far from the carbon atom is the center of mass of the molecule?

FIGURE 7-37Problem 50.

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According to Eq. 7鈥�4, the longer the impact time of an impulse, the smaller the force can be for the same momentum change, and hence the smaller the deformation of the object on which the force acts. On this basis, explain the value of air bags, which are intended to inflate during an automobile collision and reduce the possibility of fracture or death.

A 28-g bullet strikes and becomes embedded in a 1.35-kg block of wood placed on a horizontal surface just in front of the gun. If the coefficient of kinetic friction between the block and the surface is 0.28, and the impact drives the block a distance of 8.5 m before it comes to rest, what was the muzzle speed of the bullet?
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