High School

2 Fig. 2.1 shows a hammer being used to drive a nail into a piece of wood.hammer headnailwoodFig. 2.1The mass of the hammer head is 0.15 kg.The speed of the hammer head when it hits the nail is 8.0 m/s.The time for which the hammer head is in contact with the nail is 0.0015 s.The hammer head stops after hitting the nail.1.20(a) Calculate the change in momentum of the hammer head.(b) state the impulse given to nail. (c) calculate the average force between the hammer and the nail

2 Fig 2 1 shows a hammer being used to drive a nail into a piece of wood hammer headnailwoodFig 2 1The mass of the

Answer :

The change in momentum of the hammer head is -1.2 kg m/s. The impulse given to the nail is -1.2 kg m/s. The average force between the hammer and the nail is -800 N.

(a) The change in momentum of the hammer head can be calculated using the formula:

Change in Momentum = Mass x Final Velocity - Mass x Initial Velocity

Substituting the given values, the change in momentum is:

Change in Momentum = 0.15 kg x 0 m/s - 0.15 kg x 8.0 m/s = -1.2 kg m/s

(b) The impulse given to the nail can be calculated using the formula:

Impulse = Force x Time

Since the hammer head stops after hitting the nail, the impulse given to the nail would be equal to the change in momentum of the hammer head, which is -1.2 kg m/s.

(c) The average force between the hammer and the nail can be calculated using the formula:

Average Force = Impulse / Time

Substituting the given values, the average force is:

Average Force = -1.2 kg m/s / 0.0015 s = -800 N

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Given:

The mass of the hammerhead is m = 0.15 kg

The speed of the hammerhead is v = 8 m/s

The time for which the hammerhead is in contact with the nail is

[tex]\Delta t\text{ =}0.0015\text{ s}[/tex]

To find the change in momentum

The impulse and the average force.

Explanation:

The change in momentum will be

[tex]\begin{gathered} \Delta p\text{ = mv} \\ =\text{ 0.15}\times8 \\ =1.2kg\text{ m/s} \end{gathered}[/tex]

The impulse will be

[tex]\begin{gathered} Im\text{pulse = change in momentum} \\ =1.2kg\text{ m/s} \end{gathered}[/tex]

The average force will be

[tex]\begin{gathered} F_{av}=\frac{Impulse}{\Delta t} \\ =\frac{1.2}{0.0015} \\ =800\text{ N} \end{gathered}[/tex]

Final Answer: The change in momentum is 1.2 kg m/s

The impulse is 1.2 kg m/s.

The average force is 800 N