"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?

For Further Reading

* 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

This doesn't seem right...am I doing something wrong with my calculations??? PLEASE HELP :)

yOu need to use average velocity, not initial velocity. The average velocity is 1/2 the initial velocity.

distance=averagevelocity*time

Well, aren't you in a relative pickle! Let's see if we can straighten this out with a little clown logic.

For part (a), we know that block L has a release speed of 1.80 m/s relative to the floor. So, we can assume that block R has the same speed relative to the floor because they are connected by the spring. In other words, block R is just hanging on for the ride!

To find how far block R travels in the next 0.800 s, we can use the formula distance = average velocity * time. Now, the average velocity is half of the initial velocity, so we need to divide 1.80 m/s by 2. That gives us an average velocity of 0.90 m/s.

Now we can plug in the numbers and do the math. Multiply 0.90 m/s by 0.800 s and you'll get your answer. I'm not going to do it for you because I have a habit of dropping numbers, and we don't want any casualties, do we?

As for part (b), the wording is a little confusing. But fear not, clown bot is here to save the day! If the spring gives block L a release speed of 1.80 m/s relative to the velocity it gives block R, that means block R starts off with a velocity of 0 m/s. Yep, you heard that right, the poor thing doesn't move an inch!

So, the distance block R travels in the next 0.800 s would be... drumroll please... 0 meters! Block R doesn't budge. It just sits there looking pretty, while block L takes all the glory. Poor block R, always being overshadowed.

So, there you have it! I hope that clears things up for you. Remember, when it comes to relative motion, sometimes you just have to go with the flow... or lack thereof. Stay clowny!

To find the distance traveled by block R in both scenarios, we need to use the principles of conservation of momentum and average velocity.

(a) In the first scenario, where block L has a release speed of 1.80 m/s relative to the floor, we can use the conservation of momentum equation:

mL*vL = mR*vR

Here, mL = 1.90 kg, mR = 0.500 kg, and vL = 1.80 m/s (relative to the floor).

Solving for vR, we get:

vR = (mL*vL) / mR
vR = (1.90 kg * 1.80 m/s) / 0.500 kg
vR = 6.84 m/s

Now, we can find the distance traveled by block R using the average velocity:

distance = average velocity * time
distance = (1/2) * vR * t
distance = (1/2) * 6.84 m/s * 0.800 s
distance = 2.752 m

So, block R travels a distance of 2.752 m in the next 0.800 s.

(b) In the second scenario, where block L has a release speed of 1.80 m/s relative to the velocity that the spring gives block R, we can write the conservation of momentum equation as:

mL*(vL - vR) = mR*vR

Again, mL = 1.90 kg, mR = 0.500 kg, and vL = 1.80 m/s (relative to the velocity given to block R).

Solving for vR, we get:

vR = (mL*vL) / (mR + mL)
vR = (1.90 kg * 1.80 m/s) / (0.500 kg + 1.90 kg)
vR = 2.216 m/s

Now, using the average velocity to find the distance traveled by block R:

distance = average velocity * time
distance = (1/2) * vR * t
distance = (1/2) * 2.216 m/s * 0.800 s
distance = 0.888 m

So, block R travels a distance of 0.888 m in the next 0.800 s in this scenario.

Please let me know if you need further clarification or have any other questions.

To solve this problem, we need to use the principles of conservation of momentum and average velocity.

(a) The first step is to use the conservation of momentum to find the velocity of block R. The momentum of block L (mL) is equal to the momentum of block R (mR). We can express this as:

mL * velocityL = mR * velocityR

Substituting the given values, we have:

1.90 kg * 1.80 m/s = 0.500 kg * velocityR

Now we need to solve for velocityR:

velocityR = (1.90 kg * 1.80 m/s) / 0.500 kg = 6.84 m/s

(b) In this case, we need to find the relative velocity between the two blocks. This means we need to subtract the velocity of block R from the velocity of block L. Given that the initial velocity of block L relative to the velocity of block R is 1.80 m/s, the relative velocity is:

velocityLrelative = velocityL - velocityR

velocityLrelative = 1.80 m/s - 6.84 m/s = -5.04 m/s

Now, to find the distance traveled by block R in the next 0.800 s, we need to use the average velocity. The average velocity is 1/2 the initial velocity in this case:

averageVelocity = (1/2) * velocityLrelative = (1/2) * (-5.04 m/s) = -2.52 m/s

Finally, we can use the equation for distance, which is distance = averageVelocity * time:

distance = (-2.52 m/s) * 0.800 s = -2.016 m

The negative sign indicates that the distance is in the opposite direction of the initial velocity. So block R travels 2.016 m in the opposite direction of block L.