Momentum & Energy
1. Under what conditions can we apply Conservation of Mechanical Energy?
2. Under what conditions can we apply Conservation of Momentum?
3. Consider the following situation. A bullet of mass m1 is shot with
a speed of v1 toward a block of mass M2 that is at rest and attached to a
spring of constant k. The bullet enters the block and is stopped within it.
The block moves on the frictionless surface making the spring compress by
a maximum amount X.
(a) Can you correctly use Conservation of Mechanical Energy between the two
pictures above?
(b) Can you correctly use Conservation of Momentum between the two pictures?
yes
no WHY?
(c) If your answer is "No" to both of these, how can you proceed in order to determine v1, given the masses, k, and X?
(e.g. Try k = 5000 N/m, X = 16 cm, m1 = 0.050 kg, m2 = 3.95 kg, you should get v1 = 453 m/s.)
4. Carts of mass m1 and m2 are connected by a spring of constant k
initially compressed by an amount X and held together by a small string. They
move with a velocity v0 on a frictionless surface. At some time the string
is magically cut, and the masses spring apart. Find the velocities of the
two carts after they spring apart.
(a) Can you correctly use Conservation of Mechanical Energy between the two pictures above?
ΚΚΚΚΚΚΚΚΚΚ yes no WHY?(b) Can you correctly use Conservation of Momentum between the two pictures?
yes
no WHY?
(eg. K = 5000 N/m, X = 16 cm, m1 = 7.0 kg, m2 = 3.0 kg, v0 = 5.0 m/s. Answers are v1 = 2.65 m/s and v2 = 10.46 m/s.)
5. A bullet of mass 25 grams heads toward a block of wood of mass 1.500
kg. The wood can slide on a horizontal table where a friction force of 3.00
N acts. The bullet penetrates the wood and emerges at 10.0 m/s. The block
of wood slides 0.80 m along table before coming to rest. Find the speed of
the bullet initially.
6. Two carts move without friction along a horizontal surface and collide
as shown below. Before the collision m1 moves at v1 and m2 is at rest. The
collision force is provided by a spring, and a ratchet mechanism holds the
two carts together so that they move as one after the collision, and the spring,
constant k, is compressed by an amount x. I want you to find the value of
x in terms of m1, m2, v1, and k.
Hints: Does conservation of momentum apply to this problem? Does conservation
of mechanical energy apply to this problem? Solve in symbols and then try
m1 = 3 kg, m2 = 2 kg, v1 = 5 m/s, and k = 900 N/m.
| 7. A bullet of mass m1 is shot with a speed v1 toward a bale of hay of mass m2 attached to a spring of constant k. The hay stops the bullet, slides without friction and slides a distance x before momentarily stopping. Find the speed of the bullet in terms of m1, m2, k, and x. |  |