Two bodies hang on a string 2.1m long. The two bodies have a mass of 3.75kg and 2.4kg respectively. If the 3.75kg mass is raised to a height of 0.545m and released, and if upon impact the mass adhere.
Mass1 = 3.75 kg
Mass2 = 2.4 kg
String length = 2.1 m
M1 raised = 0.545m
a) Find the velocity of the 3.75kg mass before impact.
Because the potential energy (Ep) of the 3.75kg mass will be equal to its kinetic energy (Ek), the following equation can be derived to find the velocity:
E_k=1/2 mv^2
E_p=mgh
1/2 mv^2=mgh
v^2=2gh
v=¡Ì2gh
v=¡Ì(2X9.81 m⁄s^2 X0.545m)
v=¡Ì(10.69 m^2⁄s^2 )
Velocity before impact=3.27 m⁄s (Ans.)
b) Find the common velocity of the mass after impact.
Lost inE_(k1 ) before impact=Gain inE_k2 after impact
1/2 M_1 (v_1 )^2=1/2 (M_1+M_2 )X(¡¼v_2)¡½^2
0.5X3.75kgX(3.27 m⁄s)^2=0.5X(3.75kg+2.4kg)X¡¼v_2¡½^2
20.049=3.075X¡¼v_2¡½^2
¡¼v_2¡½^2=2.049/3.075
¡Ì(¡¼v_2¡½^2 )=¡Ì6.52
Velocity after impact=2.55 m⁄s (Ans.)
c) Find the lost of kinetic energy on impact.
Loss of E_k1 on impact=¡¼Ek¡½_2 after impact
E_k2=1/2(m_1+m_2)¡¼v_2¡½^2
E_k2=0.5X(3.75kg+2.4kg)X(2.55 m⁄s)^2
E_k2=3.075X¡¼2.55¡½^2
Kinetic Energy after impact=19.99J (Ans.)
d) Find the height through which the center of gravity of the system will rise.
E_p1 before impact=E_p2 after impact
m_1 gh_1=(m_1+m_2 )gh_2
3.75kgX9.81X0.545m=(3.75kg+2.4kg)X9.81Xh_2
20.05=60.33Xh_2
h_2=20.05/60.33
Final height the system will rise=0.332m (Ans.)
e) Find the tension on the string of the 3.75kg mass before impact.
Tension on the string is equal to the centrifugal force exerted by the 3.75kg mass.
F_c=(mv^2)/r
F_c=(3.75X¡¼3.27¡½^2)/2.1
F_c=40.098/2.1
F_c=19.09N (Ans.)
5 answers
Then the 3.75 kg one is lifted up .545 m
this gains U = m g h = 3.75*9.8*.545
U = 20 Joules
let it go
then just before they hit
(1/2) m v^2 = 20
v^2 = 40/3.75 = 10.7
v = 3.27 m/s
momentum = m v = 3.75*3.27 = 12.2 kg m/s
same momentum after collision but mass = 3.75+2.4 = 6.15
so v after crash = 12.2/6.15 = 2 m/s
(1/2)mv^2 = (1/2)(6.15)(4) = 12.3 Joules
If you want to find out high high they go stuck together
6.15 * 9.8 * h = 12.3
h = .204 meters
Henri
Two bodies hang on a string 2.1m long. The two bodies have a mass of 3.75kg and 2.4kg respectively. If the 3.75kg mass is raised to a height of 0.545m and released, and if upon impact the mass adhere.
Mass1 = 3.75 kg
Mass2 = 2.4 kg
String length = 2.1 m
M1 raised = 0.545m
a) Find the velocity of the 3.75kg mass before impact.
Because the potential energy (Ep) of the 3.75kg mass will be equal to its kinetic energy (Ek), the following equation can be derived to find the velocity:
E_k=1/2 mv^2
E_p=mgh
1/2 mv^2=mgh
v^2=2gh
v=¡Ì2gh
v=¡Ì(2X9.81 m⁄s^2 X0.545m)
v=¡Ì(10.69 m^2⁄s^2 )
Velocity before impact=3.27 m⁄s (Ans.)
b) Find the common velocity of the mass after impact.
Lost inE_(k1 ) before impact=Gain inE_k2 after impact
1/2 M_1 (v_1 )^2=1/2 (M_1+M_2 )X(¡¼v_2)¡½^2
0.5X3.75kgX(3.27 m⁄s)^2=0.5X(3.75kg+2.4kg)X¡¼v_2¡½^2
20.049=3.075X¡¼v_2¡½^2
¡¼v_2¡½^2=2.049/3.075
¡Ì(¡¼v_2¡½^2 )=¡Ì6.52
Velocity after impact=2.55 m⁄s (Ans.)
c) Find the lost of kinetic energy on impact.
Loss of E_k1 on impact=¡¼Ek¡½_2 after impact
E_k2=1/2(m_1+m_2)¡¼v_2¡½^2
E_k2=0.5X(3.75kg+2.4kg)X(2.55 m⁄s)^2
E_k2=3.075X¡¼2.55¡½^2
Kinetic Energy after impact=19.99J (Ans.)
d) Find the height through which the center of gravity of the system will rise.
E_p1 before impact=E_p2 after impact
m_1 gh_1=(m_1+m_2 )gh_2
3.75kgX9.81X0.545m=(3.75kg+2.4kg)X9.81Xh_2
20.05=60.33Xh_2
h_2=20.05/60.33
Final height the system will rise=0.332m (Ans.)
e) Find the tension on the string of the 3.75kg mass before impact.
Tension on the string is equal to the centrifugal force exerted by the 3.75kg mass.
F_c=(mv^2)/r
F_c=(3.75X¡¼3.27¡½^2)/2.1
F_c=40.098/2.1
F_c=19.09N (Ans.)
4 answers