Problem 1 An object with m1 = 5kg is attached to a spring of negligible mass. This mass/spring combination is then slid horizont
ally on a frictionless surface with a velocity of 5 m/s towards a stationary object with m2 = 6kg. Upon impact, the spring compresses, then we examine two cases. First, find the velocities of the two objects assuming the spring completely relaxes again after the interaction. Second, assume that m2, after they separate, slides up a frictionless incline. (a)What is the relative speed of the masses when the spring is maximally compressed?
1 answer:
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Answer:
The velocity of the gun relative to the ground is 19.66 m/s
Explanation:
Given data,
The mass of the gun, M = 15.0 kg
The mass of the bullet, m = 50 g
The velocity of the train, v = 75 km/h
= 20.83 m/s
The velocity of bullet relative to train, V' = 350 m/s
The velocity of bullet relative to ground, V = 350 + 20
= 370 m/s
According to the law of conservation of momentum,
Mv' + mV' = 0
= -1.17 m/s
Therefore, the velocity of the gun with,
v₀ = V + v'
= 20.83 - 1.17
= 19.66 m/s
Hence, the velocity of the gun relative to the ground is 19.66 m/s
Answer:
The force is 1.34 newtons and its direction is upward.
Explanation:
Choosing positive direction pointing towards the floor in this collision we're going to use the momentum-impulse theorem that states:
(1)
with the change in the momentum and J the impulse, with pi the initial momentum that is the momentum just before the collision and pf the final momentum th is the momentum just after the collision. The impulse J is also defined as:
(2)
with the average force and
the time the collision lasts
We can equate expressions (2) and (1):
Using the definition of linear momentum as mass (m) time velocity (v):
We can solve for Favg:
(3)
Now we should find the velocities vf and vi, we should do this using conservation of energy:
For the velocity the ball has just before reaches the floor:
With Ui the initial potential energy (there is not initial kinetic energy) and Kf the final kinetic energy (there is not final potential energy), then:
solving for vi:
For the velocity the ball has just after bounces the floor:
There is not initial potential energy because it's a floor level at this instant, and the there is not final kinetic energy because the ball has instantly zero velocity at its maximum height (hm), then:
solvig for vf:
Using vf and vi on (3):
The negative sign indicates the direction of the force is pointing away the floor