Respuesta :
Answer:
m1 = 0.160kg
v1 = 0.900 m/s before the collision
m2 = 0.310kg
v2 = - 2.18m/s
If final vel. of m1 is v1 and of mass m2 is v2, then
momentum is conserved
m1u1 + m2u2 = m1v1 +m2v2_____________(1)
as kinetic energy is conserved,
(1/2)m1u1^2+(1/2)m2u2^2 = (1/2)m1v1^2+(1/2)m2v2^2__(2)
solving these equations,
v1=[2 m2u2 +(m1-m2) u1] / (m1+m2)
v2 = [2 m1u1 +(m2-m1) u2] / (m1+m2)
substituting values of u1,u2 etc we get
v1 = { 2*0.310*( -2.18) + [( 0.160 -0.310)0.900] } / [ 0.142+0.310]
v1 = - 0.4847m/s
v2 = [2 m1u1 +(m2-m1) u2] / (m1+m2)
= ( 2 × 0.160×0.900+(0.320-0.160)0.310 / (0.160+ 0.310)
v2 = 0.718 m/s
Explanation:
The collision is elastic ,meaning both momentum and the kinetic energy remain conserved.we take the velocity towards the right positive and to the left negative.
Answer:
- V_a2 is 3.156 m/s in the left direction
- V_b2 is 0.076 m/s in the left direction
Explanation:
Since the 2 gliders are moving on a frictionless surface, then there is no net external force on the system and thus the collision is elastic;
In elastic collisions, the relative velocities before and after collision have the same values.
Thus,
V_a1 - V_b1 = V_b2 - V_a2
Where,
V_a1 is initial velocity of first glider
V_a2 is final velocity of first glider
V_b1 is initial velocity of second glider
V_b2 is final velocity of second glider
From the question,
V_a1 = 0.9 m/s
V_b1 = 2.18 m/s
Thus,
0.9 - (-2.18) = V_b2 - V_a2
V_b2 - V_a2 = 3.08 m/s - - - - (1)
Now, the collision equation is written as;
m_a•V_a1 + m_b•V_b1 = m_a•V_a2 + m_b•V_b2
We are given that;
m_a = 0.16kg
m_b = 0.31 kg
Thus, plugging in the values,
(0.16 x 0.9) + (-0.31 x 2.18) = 0.16•V_a2 + 0.31•V_b2
0.144 - 0.6758 = 0.16•V_a2 + 0.31•V_b2
0.16•V_a2 + 0.31•V_b2 = -0.5318
Divide through by 0.16;
V_a2 + 1.9375•V_b2 = -3.324 - - - (2)
Let's add eq1 and 2 to get;
V_b2 + 1.9375•V_b2 = 3.08 - 3.324
2.9375V_b2 = -0.224
V_b2 = -0.224/2.9375 = - 0.076 m/s
Negative sign means it is in an opposite direction which in this case is to the left.
Thus, V_b2 is 0.076 m/s in the left direction
Now, let's find V_b2.
Let's put -0.076 m/s for V_b2 in eq 1;
Thus,
-0.076 m/s - V_a2 = 3.08 m/s
V_a2 = -0.076 m/s - 3.08 m/s
V_a2 = -3.156 m/s
Negative sign means it is in an opposite direction which in this case is to the left.
Thus, V_a2 is 3.156 m/s in the left direction
