A stationary block explodes into two pieces L and R that slide across a frictionless floor and then into regions with friction, where they stop. Piece L, with a mass of 2.0 kg, encounters a coefficient of kinetic friction µL = 0.40 and slides to a stop in distance dL = 0.15 m. Piece R encounters a coefficient of kinetic friction µR = 0.50 and slides to a stop in distance dR = 0.20 m. What was the mass of the original block?
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* Physics - bobpursley, Sunday, February 25, 2007 at 5:24pm
the momentum of L and R are equal.
energyL= mu*mg*distance
then solve for velocity L (KE=energy)
knowing velocityL, you can use momentum to find veloicty R.
* Physics - COFFEE, Sunday, February 25, 2007 at 11:29pm
I did:
energyL = mu*mg*distance
energyL = (.4)(2)(9.8)(.15)
energyL = 1.176
Then,
KE = 1/2mv^2
1.176 = 1/2(2)v^2
v = 1.08 m/s
Then which equation do I use???
So the momentum sum is zero.
1.08*2+Vr*massR=0
You have to solve for Vr the same way.
1/2 Mr*Vr^2= Mur*Mr*g*Dr notice the Mr divide out, so solve for Vr. Put that in the equation
1.08*2+Vr*massR=0
solve for mass r.
Then total mass is massR+2
To find the mass of the original block, we can use the principle of conservation of momentum. Since the block is stationary before the explosion, the total momentum before the explosion is zero. Therefore, the momentum of piece L and piece R after the explosion must be equal in magnitude but opposite in direction.
First, let's calculate the velocity of piece L using the given information. The work done by friction on piece L can be calculated using the formula: work = friction force * distance. In this case, the friction force is given by the equation: forceL = µL * massL * gravity, where µL is the coefficient of kinetic friction for piece L, massL is the mass of piece L, and gravity is the acceleration due to gravity.
Using the given values, we can calculate the work done on piece L: workL = forceL * distanceL.
Since the work done on an object is equal to the change in kinetic energy, we can equate the work done on piece L to the change in kinetic energy: workL = KE L initial - KE L final.
Initially, piece L is at rest, so its initial kinetic energy (KE L initial) is zero. Piece L slides to a stop, so its final kinetic energy (KE L final) is also zero.
Equating the work done on piece L to the change in kinetic energy, we get: workL = KE L initial - KE L final = 0 - 0 = 0.
Therefore, the work done on piece L is zero and no energy is transferred to it. This means that the velocity of piece L is also zero.
Now, let's calculate the velocity of piece R using the same principle. The work done by friction on piece R can be calculated using the formula: work = friction force * distance. In this case, the friction force is given by the equation: forceR = µR * massR * gravity, where µR is the coefficient of kinetic friction for piece R, massR is the mass of piece R, and gravity is the acceleration due to gravity.
Using the given values, we can calculate the work done on piece R: workR = forceR * distanceR.
Since the work done on an object is equal to the change in kinetic energy, we can equate the work done on piece R to the change in kinetic energy: workR = KE R initial - KE R final.
Initially, piece R is at rest, so its initial kinetic energy (KE R initial) is zero. Piece R slides to a stop, so its final kinetic energy (KE R final) is also zero.
Equating the work done on piece R to the change in kinetic energy, we get: workR = KE R initial - KE R final = 0 - 0 = 0.
Therefore, the work done on piece R is zero and no energy is transferred to it. This means that the velocity of piece R is also zero.
Since the momentum of piece L and piece R is equal in magnitude and opposite in direction, and both pieces have zero velocity, we can conclude that the total momentum before the explosion is zero.
To find the mass of the original block, we can use the equation: momentum L + momentum R = 0, where momentum L is the momentum of piece L and momentum R is the momentum of piece R.
The momentum of an object is given by the equation: momentum = mass * velocity.
Since both piece L and piece R have zero velocity, their momenta are both zero.
Therefore, we can write the equation: 0 + 0 = 0.
This equation tells us that the momentum of the original block before the explosion is zero, which means that the mass of the original block must also be zero. However, this does not make physical sense.
Since the mass of the original block cannot be zero, there seems to be an error or missing information in the given problem statement. Without additional information, it is not possible to determine the mass of the original block.
To find the mass of the original block, we can follow these steps:
1. Calculate the kinetic energy of piece L using the equation: energyL = μL * m * g * dL
- Given: μL = 0.40, m = 2.0 kg, g = 9.8 m/s^2, and dL = 0.15 m
- Substitute the values into the equation: energyL = (0.40) * (2.0 kg) * (9.8 m/s^2) * (0.15 m)
- Calculate: energyL = 1.176 J
2. Use the kinetic energy equation, KE = 1/2 * m * v^2, to find the velocity of piece L.
- Given: energyL = 1.176 J and m = 2.0 kg
- Rearrange the equation to solve for v: v = √(2 * energyL / m)
- Substitute the values and calculate: v = √(2 * 1.176 J / 2.0 kg)
- Calculate: v ≈ 1.08 m/s
3. Since momentum is conserved, the momentum of piece L (pL) is equal to the momentum of piece R (pR). Use this information to find the velocity of piece R.
- Given: pL = pR and massL = 2.0 kg
- Use the momentum equation: pL = mR * vR, where mR is the unknown mass of piece R
- Rearrange the equation to solve for vR: vR = pL / mR
- Substitute the values: vR = (2.0 kg * 1.08 m/s) / mR
4. Use the equation for the work done by friction to find the mass of piece R.
- Given: μR = 0.50, g = 9.8 m/s^2, and dR = 0.20 m
- The work done by friction is W = μR * mR * g * dR
- The work done is equal to the change in kinetic energy: W = 1/2 * mR * vR^2
- Substitute the values and equation from step 3: μR * mR * g * dR = 1/2 * mR * [(2.0 kg * 1.08 m/s) / mR]^2
- Simplify the equation and solve for mR: (0.50) * (9.8 m/s^2) * (0.20 m) = 1/2 * [(2.0 kg * 1.08 m/s) / mR]^2
- Solve for mR.
5. Lastly, calculate the mass of the original block.
- The original block consists of piece L with massL = 2.0 kg and piece R with massR (as found in step 4).
- The total mass is the sum of massL and massR.
By following these steps, you can find the mass of the original block.