Two gliders are set in motion on a horizontal air track. A spring of force constant k is attached to the back end of the second glider. As shown in Figure P8.48, the first glider, of mass m1, moves to the right with speed v1, and the second glider, of mass m2, moves more slowly to the right with speed v2. When m1 collides with the spring attached to m2, the spring compresses by a distance xmax, and the gliders then move apart again. In terms of v1, v2, m1, m2, and k, find (a) the speed rat maximum compression, (b) the maximum compression xmax, and (c) the velocity of each glider after m1 has lost contact with the spring.
(a)
The speed at the maximum compression for the spring.
Answer to Problem 48P
The speed at the maximum compression for the spring is
Explanation of Solution
Write the expression for conservation of momentum.
Here,
Rewrite the above expression for mass and velocity of gliders.
Here,
Conclusion:
Rewrite the equation (II) for v.
Therefore, the speed at the maximum compression for the spring is
(b)
The maximum compression of the spring.
Answer to Problem 48P
The maximum compression of the spring is
Explanation of Solution
Write the expression for law of conservation of energy for the two gliders.
Here,
Rewrite the above expression.
Conclusion:
Substitute
Rewrite the above equation for
Therefore, the maximum compression of the spring is
(c)
The velocity of the each glider after first gliders has lost the contact with spring.
Answer to Problem 48P
The velocity of the second glider is
Explanation of Solution
Write the expression for conservation of momentum.
Here,
Write the expression for law of conservation of energy for the each gliders.
Rewrite the equation (VI).
Conclusion:
Simplify the above relation and substitute equation (V).
Substitute the above relation in equation (V) and rearrange for
Therefore, the velocity of the second glider is
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Chapter 8 Solutions
Principles of Physics
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