Respuesta :
(a) The hammer moves at a speed of [tex]v=7 m/s[/tex], covering a distance of [tex]S=1.00 cm=0.01 m[/tex]. Since it is a uniform motion, the time is given by
[tex]t= \frac{S}{v}= \frac{0.01m}{7 m/s}=1.4\cdot 10^{-3}s [/tex]
(b) first of all, let's calculate the acceleration. The hammer's speed changes from 7 m/s to 0, so [tex]\Delta v=-7 m/s[/tex]. The time interval is the one calculate at step (a), so the acceleration is
[tex]a= \frac{\Delta v}{\Delta t}= \frac{-7 m/s}{1.4 \cdot 10^{-3} s}=-4900 m/s^2 [/tex]
where the negative sign means it is a deceleration.
Finally we can find the force by using Newton's second law. We are interested only in its magnitude, so we can neglect the negative sign. We have:
[tex]F=ma=(0.450 kg)(4900 m/s^2)=2205 N[/tex]
[tex]t= \frac{S}{v}= \frac{0.01m}{7 m/s}=1.4\cdot 10^{-3}s [/tex]
(b) first of all, let's calculate the acceleration. The hammer's speed changes from 7 m/s to 0, so [tex]\Delta v=-7 m/s[/tex]. The time interval is the one calculate at step (a), so the acceleration is
[tex]a= \frac{\Delta v}{\Delta t}= \frac{-7 m/s}{1.4 \cdot 10^{-3} s}=-4900 m/s^2 [/tex]
where the negative sign means it is a deceleration.
Finally we can find the force by using Newton's second law. We are interested only in its magnitude, so we can neglect the negative sign. We have:
[tex]F=ma=(0.450 kg)(4900 m/s^2)=2205 N[/tex]
(a) The duration of impact of the hammer is [tex]\fbox{\begin\\1.43 \times {10^{ - 3}}\,{\text{s}}\end{minispace}}[/tex] .
(b) The average force exerted on the nail is [tex]\fbox{\begin\\2205\,{\text{N}}\end{minispace}}[/tex].
Further explanation:
When hammer hit the nail it got impacted by the hit and get into the board. This insertion in the board take time which is called duration of impact. The force exerted on the nail is directly proportional to the acceleration of the nail.
Given:
The speed of hammer is [tex]7\,{\text{m/s}}[/tex].
The distance of nail which is inserted in the board is [tex]1\,{\text{cm}}[/tex].
The mass of the hammer is [tex]0.450\,{\text{Kg}}[/tex].
Concept used:
The rate of change of displacement of a body in unit time is called speed of the body. It is a scalar quantity.
The expression for the speed of the body is given as.
[tex]v = \dfrac{s}{t}[/tex]
Rearrange the above expression for the time.
[tex]t=\dfrac{s}{v}[/tex] …… (1)
Here, [tex]s[/tex] is the distance covered, [tex]v[/tex] is the speed of body and [tex]t[/tex] is the time.
According to Newton’s second law of motion “the rate of change of momentum is equal to the force applied on the body.”
The expression for the newton’s law is given as.
[tex]F = ma[/tex] ……. (2)
The expression for the acceleration of the body is given as.
[tex]\fbox{\begin\\a = \dfrac{{\left( {v - u} \right)}}{t}\end{minispace}}[/tex] …… (3)
Here, [tex]u[/tex] is the initial velocity and [tex]v[/tex] is the final velocity.
Substitute [tex]1\,{\text{cm}}[/tex] for [tex]s[/tex] and [tex]7\,{\text{m/s}}[/tex] for [tex]v[/tex] in equation (1).
[tex]\begin{aligned}t&=\frac{{1\,{\text{cm}}}}{{7\,{\text{m/s}}}}\\&=\frac{{1\,{\text{cm}}\left( {\frac{{1\,{\text{m}}}}{{100\,{\text{cm}}}}} \right)}}{{7\,{\text{m/s}}}}\\&=1.43 \times {10^{ - 3}}\,{\text{s}} \\ \end{aligned}[/tex]
Substitute [tex]1.43 \times {10^{ - 3}}\,{\text{s}}[/tex] for [tex]t[/tex], for[tex]0\,{\text{m/s}}[/tex] and [tex]v[/tex] for in equation (3).
[tex]\begin{gathered}a= \frac{{\left( {0\,{\text{m/s}} - 7\,{\text{m/s}}} \right)}}{{\left( {1.43 \times {{10}^{ - 3}}\,{\text{s}}} \right)}} \\= \left( { - 4900\,{\text{m/}}{{\text{s}}^{\text{2}}}} \right) \\ \end{gathered}[/tex]
Substitute[tex]\left( { - 4900\,{\text{m/}}{{\text{s}}^{\text{2}}}} \right)[/tex] for [tex]a[/tex] and [tex]0.450\,{\text{Kg}}[/tex] for [tex]m[/tex] in equation (2).
[tex]\begin{aligned}F&=\left( {0.450\,{\text{Kg}}} \right)\left( { - 4900\,{\text{m/}}{{\text{s}}^{\text{2}}}} \right)\\&=- 2209\,{\text{N}} \\ \end{aligned}[/tex]
Thus, the duration of impact is[tex]1.43 \times {10^{ - 3}}\,{\text{s}}[/tex] and the force exerted on the nail is [tex]2209\,{\text{N}}[/tex] in the opposite direction.
Learn more:
1. Motion under friction https://brainly.com/question/7031524.
2. Conservation of momentum https://brainly.com/question/9484203.
3. Force on a body https://brainly.com/question/6125929.
Answer Details:
Grade: College
Subject: Physics
Chapter: Kinematics
Keywords:
Acceleration, force, acceleration due to gravity, friction, normal, weight, mass, motion, impact, nail, hammer, acceleration, duration of impact, 0.450 kg, 7 m/s, 2205 N,1.429*10^-3 sec, 1.43*10^-3 sec.
