The collision between a hammer and a nail can be considered to be approximately
ID: 1357872 • Letter: T
Question
The collision between a hammer and a nail can be considered to be approximately elastic.
Part A
Calculate the kinetic energy acquired by a 14-g nail when it is struck by a 530-g hammer moving with an initial speed of 4.8 m/s .
Express your answer using two significant figures.
The collision between a hammer and a nail can be considered to be approximately elastic.
Part A
Calculate the kinetic energy acquired by a 14-g nail when it is struck by a 530-g hammer moving with an initial speed of 4.8 m/s .
Express your answer using two significant figures.
Explanation / Answer
Solution: Let the speed of the hammer before collision be vhi = 4.8m/s
speed of the nail before collision be vni = 0 m/s (stationary)
speed of the hammer after collision be vhf
speed of the nail before collision be nf
mass of the hammer mh = 530 g = 0.53 kg
mass of the nail mn = 14 g = 0.014 kg
During the elastic collision, the total linear momentum is conserved, thus
Total momentum before collision = total momentum after collision
mh*vhi + mn*vni = mh*vhf + mn*vnf
mh*vhi = mh*vhf + mn*vnf since vni = 0
mh*(vhi - vhf ) = mn*vnf ------------------------------------(1)
During the elastic collision the total kinetic energy is also conserved ,
Total kinetic energy before collision = total kinetic energy after collision
(1/2)mh*vhi2 + (1/2)mn*vni2 = (1/2)mh*vhf2 +(1/2) mn*vnf2
mh*vhi2 + 0 = mh*vhf2 + mn*vnf2
mh*(vhi2 - vhf2 )= mn*vnf2
mh*(vhi + vhf ) *(vhi - vhf )= mn*vnf2 ------------------------------------------------------(2)
divide equation(2) by (1) we get
(vhi + vhf ) = vnf
vhf = vnf - vhi
Putting this vhf in equation (1) we get
mh*(vhi - vnf + vhi ) = mn*vnf
mh*2vhi – mh*vnf = mn*vnf
mh*2vhi = mn*vnf + mh*vnf
mh*2vhi = vnf*(mn +mh)
vnf = 2mhvhi/(mn +mh)
Thus
vnf = (2*0.53kg*4.8m/s) / (0.014+0.53)kg
vnf = 9.3529 m/s
Thus the kinetic energy of the nail is
KEnf = (1/2) mn*vnf2
KEnf = (1/2)*0.014kg*(9.3529m/s)2
KEnf = 0.6123 J
Thus the kinetic energy acquired by the nail is 0.61 J