after an ice show, Michelle helps clear the props from the ice. Standing in her skates next to a potted artifical tree, she gives it a push. The tree, which has a mass of 6500g, slides forward at a velocity of 13m/s. Michelle, with a mass of 40.0kg, slides in the opposite direction. What is Michelle's velocity after pushing the tree?
0= m1•v1- m2•v2
v2 =m1•v1/m2 =6.5•13/40 =2.11 m/s
To find Michelle's velocity after pushing the tree, we can use the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, as long as no external forces are acting on the system.
In this scenario, we have Michelle and the artificial tree as the system. Before the push, the tree was at rest, so its initial momentum is zero. Michelle, on the other hand, has an initial velocity of unknown magnitude in the opposite direction.
After the push, the tree slides forward at a velocity of 13 m/s, so its final momentum is (mass of tree) * (velocity of tree) = 6500 g * 13 m/s. Michelle, with a mass of 40.0 kg, slides in the opposite direction, so her final momentum is (mass of Michelle) * (velocity of Michelle).
By applying the conservation of momentum principle, we can write the equation:
(tree's initial momentum) + (Michelle's initial momentum) = (tree's final momentum) + (Michelle's final momentum)
0 + (mass of Michelle) * (velocity of Michelle) = (mass of tree) * (velocity of tree) + 0
As we want to solve for Michelle's final velocity, we can rearrange the equation:
(mass of Michelle) * (velocity of Michelle) = (mass of tree) * (velocity of tree)
(40.0 kg) * (velocity of Michelle) = (6500 g) * (13 m/s)
Now, let's convert the mass of the tree to kilograms:
(40.0 kg) * (velocity of Michelle) = (6.5 kg) * (13 m/s)
To find the velocity of Michelle, we can isolate the variable:
(velocity of Michelle) = (6.5 kg * 13 m/s) / (40.0 kg)
Performing the calculation:
(velocity of Michelle) = 8.45 m/s
Therefore, Michelle's velocity after pushing the tree is 8.45 m/s.