Calculating Speed in a Tug-of-War on Ice

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In summary, James and Ramon, with masses of 90.0 kg and 60.0 kg respectively, are standing 20.0 m apart on a frozen pond. Ramon pulls on a rope to give himself a speed of 0.70 m/s. Using the concept of center of mass, we can find that James's speed is also 0.70 m/s after the pull, as the two are part of the same system and experience equal and opposite forces according to Newton's third law. This is equivalent to using the conservation of momentum equation, but considering the velocity of the center of mass instead of individual velocities. This is also evident in a separate problem where two people of equal mass and distance apart perform a
  • #1
iwonde
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James and Ramon are standing 20.0 m apart on the slippery surface of a frozen pond. Ramon has mass 60.0 kg and James has mass 90.0 kg. Ramon pulls on the rope to give himself a speed of 0.70 m/s. What is James's speed?

From what I understand, since there is an external force due to Ramon's pull, momentum is not conserved, and I can't use the conservation of momentum equation. So, I'm thinking this is a center of mass problem, with V_cm = 0.70 m/s, and James's speed is 0.70 m/s. However, that's not the correct answer. Can anyone help me with this?
 
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  • #2
Well, there's certainly an "external" force on James, if you consider James and Ramon as separate systems. But what if you consider them as parts of the same system?

Alternatively, consider Newton's 3rd law: Whatever force that Ramon exerts on James must equal the force that James exerts on Ramon.

You can view this as a center of mass problem (note that this is equivalent to using conservation of momentum). But what makes you think that the V_cm = 0.70 m/s? That's James's speed after the pull, not the velocity of the cm.
 
  • #3
It turns out that I have to use center of mass for this problem.
What I have so far:
(m_J)(v_J)+(m_R)(v_R)=(m_J + m_R)V_cm
The thing is, I have two unknowns here: v_J and V_cm. I suppose v_J is what I'm solving for. I'm stuck.
 
  • #4
first solve this prob to get a better understanding...

Two people of equal mass, 6 meters apart, attempt a tug of war on frictionless ice. If they pull on opposite ends of the rope with equal forces, each slides 3 meters to a point midway between them.Suppose instead that only one person pulls and the other fastens the rope around his or her waist. How for does each person slide? (Neglect any effects of the rope's mass.)
 
  • #5
iwonde said:
It turns out that I have to use center of mass for this problem.
What I have so far:
(m_J)(v_J)+(m_R)(v_R)=(m_J + m_R)V_cm
The thing is, I have two unknowns here: v_J and V_cm. I suppose v_J is what I'm solving for. I'm stuck.
What you're using is conservation of momentum. And you are given V_cm: They start from rest. :wink:
 
  • #6
Thanks, guys! I got it! =)
 

1. What is a tug-of-war on the ice?

A tug-of-war on the ice is a game or competition where two teams or groups of individuals pull on opposite ends of a rope that is placed on an icy surface. The goal is to try and pull the other team or group across a designated line or marker.

2. How is a tug-of-war on the ice different from a traditional tug-of-war?

A tug-of-war on the ice is different from a traditional tug-of-war in the sense that it is played on an icy surface, which adds an extra challenge and requires different strategies for winning. It also requires specialized equipment, such as special shoes or cleats, to prevent slipping on the ice.

3. What are some safety precautions that should be taken during a tug-of-war on the ice?

Some safety precautions that should be taken during a tug-of-war on the ice include making sure the ice is thick enough to support the weight of the participants, having proper equipment and clothing for the icy conditions, and ensuring that the rope is securely anchored. It is also important to have a designated safety person and to stop the game immediately if anyone falls or gets injured.

4. Can anyone participate in a tug-of-war on the ice?

While anyone can participate in a tug-of-war on the ice, it is important to have proper training and experience in order to safely compete. This is especially true for competitive or professional tug-of-war on the ice events, where participants must be physically fit and have the necessary skills to compete.

5. What are some potential benefits of participating in a tug-of-war on the ice?

Participating in a tug-of-war on the ice can provide a fun and challenging physical activity that can improve strength, coordination, and teamwork skills. It can also be a unique and exciting way to stay active during the winter months and can promote a sense of camaraderie among participants.

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