"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?
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.
1.9*1.8=.5*velocityR
velocityR = 6.84 m/s
d=v*time
d=(6.84)(.8)
d=5.472m ???
To solve this problem, you need to apply the principles of conservation of momentum and kinematics.
(a) In this case, the spring gives block L a release speed of 1.80 m/s relative to the floor. The first step is to find the velocity of block R relative to the floor. Since momentum is conserved, the momentum of block L is equal to the momentum of block R.
Momentum of block L = mass of block L * velocity of block L
Momentum of block R = mass of block R * velocity of block R
Given: mass of block L (mL) = 1.90 kg
mass of block R (mR) = 0.500 kg
velocity of block L relative to the floor = 1.80 m/s
Using the principle of conservation of momentum:
mass of block L * velocity of block L = mass of block R * velocity of block R
Substituting the given values:
1.90 kg * 1.80 m/s = 0.500 kg * velocity of block R
Now, solve for the velocity of block R:
velocity of block R = (1.90 kg * 1.80 m/s) / 0.500 kg
Simplifying:
velocity of block R = 6.84 m/s
Next, to find the distance traveled by block R in the next 0.800 s, we can use the formula:
distance = velocity * time
Given: time (t) = 0.800 s
Substituting the values:
distance = 6.84 m/s * 0.800 s
Simplifying:
distance = 5.472 m
Therefore, block R travels a distance of 5.472 m in the next 0.800 s.
(b) In this case, 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 conservation of momentum principle as in part (a), the momentum of block L is still equal to the momentum of block R. However, the given velocity of block L relative to block R is needed.
Given: velocity of block L relative to block R = 1.80 m/s
Using the principle of conservation of momentum:
mass of block L * velocity of block L = mass of block R * (velocity of block R + velocity of block L relative to block R)
Substituting the given values:
1.90 kg * 1.80 m/s = 0.500 kg * (velocity of block R + 1.80 m/s)
Now, solve for the velocity of block R:
velocity of block R = (1.90 kg * 1.80 m/s - 0.500 kg * 1.80 m/s) / 0.500 kg
Simplifying:
velocity of block R = 5.52 m/s
Using the same formula as in part (a):
distance = velocity * time
Given: time (t) = 0.800 s
Substituting the values:
distance = 5.52 m/s * 0.800 s
Simplifying:
distance = 4.416 m
Therefore, block R travels a distance of 4.416 m in the next 0.800 s when block L has a release speed of 1.80 m/s relative to the velocity that the spring gives block R.