"Relative" is an important word. Block L of mass mL = 1.90 kg and block R of mass mR = 0.500 kg are held in place with a compressed spring between them. When the blocks are released, the spring sends them sliding across a frictionless floor. (The spring has negligible mass and falls to the floor after the blocks leave it.)
(a) If the spring gives block L a release speed of 1.80 m/s relative to the floor, how far does block R travel in the next 0.800 s?
(b) If, instead, the spring gives block L a release speed of 1.80 m/s relative to the velocity that the spring gives block R, how far does block R travel in the next 0.800 s?
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* Physics - bobpursley, Sunday, February 25, 2007 at 5:22pm
Momentum L has is equal to the momentum R has.
1.90*1.80=.500*veloictyR
Relative to each other, velocityLrelative=VelocityRrelative
Now to compute the distance here, obviously the relative distances are of no value....they equal each other. Here you have to convert to an absolute relative to floor velocity. AGain, use the principle that the center of gravity is constant, or, the momentums are equal.
* Physics - COFFEE, Sunday, February 25, 2007 at 11:47pm
1.9*1.8=.5*velocityR
velocityR = 6.84 m/s
d=v*time
d=(6.84)(.8)
d=5.472m ???
To find the answers to the given questions, we can use principles of momentum and relative velocities. Here's how to solve them:
(a) In this part, we need to find how far block R travels in the next 0.800 s, given that the spring gives block L a release speed of 1.80 m/s relative to the floor.
We can start by using the principle of conservation of momentum. According to this principle, the momentum of block L is equal to the momentum of block R before they start sliding. The momentum of an object is given by the product of its mass and velocity.
So, we have:
mL * vL = mR * vR
Substituting the given values:
(1.90 kg) * (1.80 m/s) = (0.500 kg) * vR
Solving for vR:
vR = (1.90 * 1.80) / 0.500
= 6.84 m/s
Now, we can find the distance block R travels using the formula:
distance = velocity * time
dR = vR * 0.800 s
= (6.84 m/s) * (0.800 s)
= 5.472 m
Therefore, block R travels approximately 5.472 meters in the next 0.800 seconds.
(b) In this part, we need to find how far block R travels in the next 0.800 s, given that the spring gives block L a release speed of 1.80 m/s relative to the velocity that the spring gives block R.
Using the same principle of conservation of momentum, we have:
mL * (vL - vR) = mR * 0
Since block R starts with a velocity of 0 relative to itself, we set its velocity as 0.
Substituting the given values:
(1.90 kg) * (1.80 m/s - 0) = (0.500 kg) * 0
Solving for vR:
vR = 1.90 * 1.80 / 0.500
= 6.84 m/s
Now, we can find the distance block R travels using the same formula:
dR = vR * 0.800 s
= (6.84 m/s) * (0.800 s)
= 5.472 m
Therefore, block R travels approximately 5.472 meters in the next 0.800 seconds, regardless of the relative velocity between the blocks.