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Two masses move along the frictionless x-axis. m₁=13.7kg is initially moving with a velocity v₁ = m₂ 13.5kg is initially at rest at the origin. There is a massless spring with spring constant k = 6410 attached to m₂. In this problem we want to find both the compression of the spring when the masses are closest together. We will assume that all motion only happens in the x-direction. (The input below will accept answers with no more than 1% variation from the correct value.) What is the momentum of the two masses before the collision? When they are closest? After the collision? before = 238.4 kgi Pclosest = 238.4 kgi Pafter = 238.4 kgi The masses are initially getting closer together, and after the collision the masses will be moving away from each other. The transition between these two situations is when the masses will be at their closest point. Thus, this must occur when ₁ = ₂. Using the fact that ₁ ₁8.7 ₂8.7 What is the relation expressing the conservation of momentum at the moment the masses are closest? 238.4 |kg = 13.7 kg ₁ + 13.5 kg U₂ 17.4. = 7₂ what are the velocities of the two masses at the moment they are closest? mi S m S

Two masses move along the frictionless x-axis. m₁=13.7kg is initially moving with a velocity v₁ = m₂ 13.5kg is initially at rest at the origin. There is a massless spring with spring constant k = 6410 attached to m₂. In this problem we want to find both the compression of the spring when the masses are closest together. We will assume that all motion only happens in the x-direction. (The input below will accept answers with no more than 1% variation from the correct value.) What is the momentum of the two masses before the collision? When they are closest? After the collision? before = 238.4 kgi Pclosest = 238.4 kgi Pafter = 238.4 kgi The masses are initially getting closer together, and after the collision the masses will be moving away from each other. The transition between these two situations is when the masses will be at their closest point. Thus, this must occur when ₁ = ₂. Using the fact that ₁ ₁8.7 ₂8.7 What is the relation expressing the conservation of momentum at the moment the masses are closest? 238.4 |kg = 13.7 kg ₁ + 13.5 kg U₂ 17.4. = 7₂ what are the velocities of the two masses at the moment they are closest? mi S m S

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Two masses move along the frictionless x-axis. m₁ = 13.7kg is initially moving with a velocity v₁ = 17.4. m₂ = 13.5kg is initially at rest at the origin. There is a massless spring with spring constant k = 6410 attached to m₂. In this problem we want to find both the compression of the spring when the masses are closest together. We will assume that all motion only happens in the x-direction. (The input below will accept answers with no more than 1% variation from the correct value.) What is the momentum of the two masses before the collision? When they are closest? After the collision? Pbefore = 238.4 kg i Pclosest = 238.4 Pafter 238.4 kg kgi The masses are initially getting closer together, and after the collision the masses will be moving away from each other. The transition between these two situations when the masses will be at their closest point. Thus, this must occur when ₁ = ₂. What is the relation expressing the conservation of momentum at the moment the masses are closest? 238.4 kg = 13.7 kg V₁ + 13.5 kg U₂ Using the fact that 7₁ = 7₂ what are the velocities of the two masses at the moment they are closest? V₁ = 8.7 m V₂ = 8.7 i What is the initial kinetic energy of the masses? What is the kinetic energy when the masses are closest? 2074 KEbefore = J KEclosest = J You should notice that the momentum before, after and when the masses are the closest is the same. However, the kinetic energy before and after the collision are the same, but the total kinetic energy when the masses are closest is less. This is because some of that energy has been converted into spring potential energy. How much work was done by the spring between the start and the instant the masses are closest? What is the change in the spring's potential energy? WST -1029 spring ΔΡΕ= 1029 J J By how much has the spring been compressed when the masses are closest? Al= m
Transcribed Image Text:Two masses move along the frictionless x-axis. m₁ = 13.7kg is initially moving with a velocity v₁ = 17.4. m₂ = 13.5kg is initially at rest at the origin. There is a massless spring with spring constant k = 6410 attached to m₂. In this problem we want to find both the compression of the spring when the masses are closest together. We will assume that all motion only happens in the x-direction. (The input below will accept answers with no more than 1% variation from the correct value.) What is the momentum of the two masses before the collision? When they are closest? After the collision? Pbefore = 238.4 kg i Pclosest = 238.4 Pafter 238.4 kg kgi The masses are initially getting closer together, and after the collision the masses will be moving away from each other. The transition between these two situations when the masses will be at their closest point. Thus, this must occur when ₁ = ₂. What is the relation expressing the conservation of momentum at the moment the masses are closest? 238.4 kg = 13.7 kg V₁ + 13.5 kg U₂ Using the fact that 7₁ = 7₂ what are the velocities of the two masses at the moment they are closest? V₁ = 8.7 m V₂ = 8.7 i What is the initial kinetic energy of the masses? What is the kinetic energy when the masses are closest? 2074 KEbefore = J KEclosest = J You should notice that the momentum before, after and when the masses are the closest is the same. However, the kinetic energy before and after the collision are the same, but the total kinetic energy when the masses are closest is less. This is because some of that energy has been converted into spring potential energy. How much work was done by the spring between the start and the instant the masses are closest? What is the change in the spring's potential energy? WST -1029 spring ΔΡΕ= 1029 J J By how much has the spring been compressed when the masses are closest? Al= m
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