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???
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* RE: PHYSICS - bobpursley, Monday, February 26, 2007 at 6:14pm
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
>>>>>>>>>>>>>>>>>>>>>>>>>>>>.
How can I find mass R if I don't have velocity R or KE of R??? I am having a lot of difficulty on here lately :(
1/2 Mr*Vr^2= Mur*Mr*g*Dr notice the Mr divide out, so solve for Vr.
Is is possible you are looking for the answer, and not reading the steps?
To find the mass of the original block, we can use the principles of conservation of momentum and energy. Here are the steps to solve the problem:
1. Start by using the principle of conservation of momentum. Since the block was initially stationary, the total momentum before the explosion is zero. Therefore, the momentum of piece L and piece R after the explosion should be equal.
2. Next, let's calculate the kinetic energy of piece L, which stops in distance dL. The formula for kinetic energy is KE = 1/2 * mass * velocity^2. We know the mass of piece L (2.0 kg) and the distance it stops (dL = 0.15 m). We can use the formula KE = µL * mg * dL to find the energy. Here, µL is the coefficient of kinetic friction for piece L, which is given as 0.40, g is the acceleration due to gravity (9.8 m/s^2), and m is the mass of piece L (2.0 kg).
3. Solve the equation from step 2 for the velocity of piece L. Rearranging the equation, we get velocityL = sqrt(2 * KE / m). Substitute the values of KE and m to find the velocity of piece L.
4. Now, we can use the principle of conservation of momentum again to find the velocity of piece R. Since the momentum of L and R are equal, we can write mvL = mvR, where vL and vR are the velocities of L and R respectively.
5. Rearrange the equation from step 4 to solve for vR. You should get vR = -2 * vL.
6. Finally, we can find the mass of piece R. We have the coefficient of kinetic friction µR and the distance it slides to a stop dR. We know that the formula for kinetic energy is the same as before: KE = 1/2 * mass * velocity^2. We can use the formula KE = µR * mg * dR to find the energy.
7. Rearrange the equation from step 6 to solve for the mass of piece R. You should get massR = µR * g * dR / vR^2.
8. The mass of the original block is the sum of the masses of piece L and piece R, so you can calculate it by adding massR to twice the mass of piece L.
By following these steps and plugging in the given values, you should be able to find the mass of the original block.