"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 :)
For Further Reading
* Re: PHYSICS - bobpursley, Tuesday, February 27, 2007 at 7:17am
yOu need to use average velocity, not initial velocity. The average velocity is 1/2 the initial velocity.
distance=averagevelocity*time
So I did...
d=(-1.8+6.84)(.8)
d=2.016m
This is wrong. What am I doing wrong?
"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?
"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?
****Momentum is conserved: mL*vL=mR*Vr implies that
Vr=mL/mR *vL= 1.90/.500 (1.80) = 6.84 m/s
distanceR=6.84*.800=5.47 meters with respect to the floor.
(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 is conserved: mL*vL=mR*Vr implies that
Vr=mL/mR *vL= 1.90/.500 (1.80) = 6.84 m/s with respect to the velocity given L
At this point, consider the words "relative to the velocity that the spring gives block R." That means to me, L is moving at 1.84 less than R is moving to the right. If R is fixed, then L is moving 1.84 to the left. If R is moving 10m/s to the right, then L is moving 10-1.84 to the RIGHT.
Here, vL=vR-1.84 where vL, vR are relative to floor.
and vR= 6.84-vL where vL,vR are relative to floor.
So vR= 6.84-vL = 6.84-vR+1.84
vR= 4.34 m/s
check my thinking and math.
Well, it looks like you've got the right idea about momentum being conserved! But for part (b), you seem to have gotten a bit confused with the relative velocities. Don't worry, it happens to the best of us!
To clarify, when it says "the spring gives block L a release speed of 1.80 m/s relative to the velocity that the spring gives block R," it means that block L's velocity is 1.80 m/s less than block R's velocity.
So, let's say block R is moving at a velocity of vR. According to the given information, block L's velocity (vL) would be vR - 1.80 m/s.
Now, we can use the equation for momentum conservation, just like before. mL * vL = mR * vR. But this time, we'll substitute vL with vR - 1.80 m/s.
Simplifying the equation, we get:
(1.90 kg) * (vR - 1.80 m/s) = (0.500 kg) * vR
Now, let's solve for vR.
1.90vR - 3.42 = 0.500vR
1.90vR - 0.500vR = 3.42
1.40vR = 3.42
vR = 3.42 / 1.40
vR ≈ 2.44 m/s
Since block R's velocity is now 2.44 m/s (relative to the floor), we can find the distance it travels in the next 0.800 s using the equation d = v * t:
d = (2.44 m/s) * (0.800 s)
d ≈ 1.95 meters
So, in this case, block R travels approximately 1.95 meters in the next 0.800 s. Keep up the good work, and remember, don't let those relative velocities trip you up!
(a) The spring gives block L a release speed of 1.80 m/s relative to the floor. To find how far block R travels in the next 0.800 s, we first need to find the velocity of block R. Using the principle of conservation of momentum, we can set up the following equation:
mL * vL = mR * vR
where mL = 1.90 kg is the mass of block L, vL = 1.80 m/s is the release speed of block L, mR = 0.500 kg is the mass of block R, and vR is the velocity of block R.
Simplifying the equation, we have:
1.90 kg * 1.80 m/s = 0.500 kg * vR
Solving for vR, we get:
vR = (1.90 kg * 1.80 m/s) / 0.500 kg
= 6.84 m/s
Now, to find the distance block R travels in the next 0.800 s, we can use the formula:
distanceR = velocityR * time
where time = 0.800 s.
Plugging in the values, we get:
distanceR = 6.84 m/s * 0.800 s
= 5.472 m
So, block R travels a distance of 5.472 meters relative to the floor.
(b) If the spring gives block L a release speed of 1.80 m/s relative to the velocity that the spring gives block R, we need to determine the velocity of block R relative to the velocity given to block L.
Using the principle of conservation of momentum and the fact that block R is moving at a velocity that is 1.84 m/s greater than block L, we can set up the following equations:
mL * vL = mR * (vR - 1.84 m/s)
mL * (vR + 1.84 m/s) = mR * vR
Solving these equations simultaneously, we can find the values of vR and vL.
First, let's solve for vR:
mL * vL = mR * (vR - 1.84 m/s)
1.90 kg * 1.80 m/s = 0.500 kg * (vR - 1.84 m/s)
3.42 kg·m/s = 0.500 kg * vR - 0.500 kg * 1.84 m/s
0.500 kg * vR = 3.42 kg·m/s + 0.500 kg * 1.84 m/s
0.500 kg * vR = 3.42 kg·m/s + 0.920 kg·m/s
0.500 kg * vR = 4.34 kg·m/s
vR = 4.34 kg·m/s / 0.500 kg
vR = 8.68 m/s
Now, let's solve for vL:
mL * (vR + 1.84 m/s) = mR * vR
1.90 kg * (8.68 m/s + 1.84 m/s) = 0.500 kg * 8.68 m/s
1.90 kg * 10.52 m/s = 4.34 kg·m/s
To find the distance block R travels in the next 0.800 s, we can use the same formula as before:
distanceR = velocityR * time
Plugging in the values, we get:
distanceR = 8.68 m/s * 0.800 s
= 6.944 m
So, block R travels a distance of 6.944 meters relative to the velocity given to block L
To solve this problem, you need to understand the concept of relative velocity. "Relative" means that you are comparing the velocities of the blocks with respect to each other or with respect to the floor.
(a) For the first part, you are given that block L has a release speed of 1.80 m/s relative to the floor. You want to find the distance block R travels in the next 0.800 s.
The first step is to use the principle of conservation of momentum, which states that the momentum of block L is equal to the momentum of block R. The equation for momentum is mL * vL = mR * vR.
Substituting the given values, we have (1.90 kg) * (1.80 m/s) = (0.500 kg) * vR.
Solving for vR, we find vR = 6.84 m/s.
To find the distance block R travels, we can use the formula distance = velocity * time. Plugging in the values, we have distanceR = (6.84 m/s) * (0.800 s) = 5.47 meters.
Therefore, block R travels a distance of 5.47 meters relative to the floor.
(b) For the second part, you are given that block L has a release speed of 1.80 m/s relative to the velocity that the spring gives block R. You want to find the distance block R travels in the next 0.800 s.
Here, we need to consider the words "relative to the velocity that the spring gives block R." This means that block L is moving 1.84 m/s slower than block R. In other words, if block R is moving at velocity vR, then block L is moving at velocity vR - 1.84 m/s. So we can write vL = vR - 1.84.
Using the principle of conservation of momentum, we have mL * vL = mR * vR. Substituting vL = vR - 1.84, we have (1.90 kg) * (vR - 1.84 m/s) = (0.500 kg) * vR.
Solving for vR, we find vR = 4.34 m/s.
To find the distance block R travels, we use the formula distance = velocity * time. Plugging in the values, we have distanceR = (4.34 m/s) * (0.800 s) = 3.47 meters.
Therefore, block R travels a distance of 3.47 meters relative to the floor.
In summary, for part (a), block R travels 5.47 meters relative to the floor, and for part (b), block R travels 3.47 meters relative to the floor.