Respuesta :
Answer:
(a). The magnitude and direction of the velocity of the otters after collision is 1.35 m/s toward left.
(b). The mechanical energy dissipates during this play is 226.98 J.
Explanation:
Given that,
Mass of one otter = 8.50 kg
Speed = 6.00 m/s
Mass of other = 5.75 kg
Speed = 5.50 m/s
(a). We need to calculate the magnitude and direction of the velocity of these free-spirited otters right after they collide
Using conservation of momentum
[tex]m_{1}v_{1}+m_{2}v_{2}=(m_{1}+m_{2})v[/tex]
Put the value into the formula
[tex]8.50\times(-6.00)+5.75\times5.50=(8.50+5.75)\times v[/tex]
[tex]v=\dfrac{-19.375}{14.25}[/tex]
[tex]v=-1.35\ m/s[/tex]
Negative sign shows the direction of motion of the object after collision is toward left.
(b). We need to calculate the initial kinetic energy
Using formula of kinetic energy
[tex]K.E_{i}=\dfrac{1}{2}m_{1}v_{1}^2+\dfrac{1}{2}m_{2}v_{2}^2[/tex]
Put the value into the formula
[tex]K.E_{i}=\dfrac{1}{2}\times8.50\times(6.00)^2+\dfrac{1}{2}\times5.75\times(5.50)^2[/tex]
[tex]K.E_{i}=239.96\ J[/tex]
We need to calculate the final kinetic energy
Using formula of kinetic energy
[tex]K.E_{f}=\dfrac{1}{2}(m_{1}+m_{2})v^2[/tex]
Put the value into the formula
[tex]K.E_{f}=\dfrac{1}{2}\times(8.50+5.75)\times(-1.35)^2[/tex]
[tex]K.E_{f}=12.98\ J[/tex]
We need to calculate the mechanical energy dissipates during this play
Using formula of loss of mechanical energy
[tex]\Delta K.E=K.E_{f}-K.E_{i}[/tex]
Put the value into the formula
[tex]\Delta K.E=12.98-239.96[/tex]
[tex]\Delta K.E=-226.98\ J[/tex]
Negative sign shows the loss of mechanical energy
Hence, (a). The magnitude and direction of the velocity of the otters after collision is 1.35 m/s toward left.
(b). The mechanical energy dissipates during this play is 226.98 J.
Answer:
Explanation:
m1 = 8.5 kg
m2 = 5.75 kg
u1 = - 6 m/s
u2 = 5.5 m/s
(a) Let the velocity after collision is v.
Use the conservation of momentum
m1 x u1 + m2 x u2 = (m1 + m2) x v
- 8.5 x 6 + 5.75 x 5.5 = (8.5 + 5.75) x v
- 51 + 31.625 = 14.25 v
v = - 1.36 m/s
So, it moves towards left after collision.
(b) Kinetic energy before collision,
Ki = 0.5 x 8.5 x 6 x 6 + 0.5 x 5.75 x 5.5 x 5.5 = 240 J
Kinetic energy after collision
Kf = 0.5 x (8.5 + 5.75) x 1.36 x 1.36 = 13.18 J
Change in energy = 240 - 13.18 = 226.82 J
