There are two set pieces in a theater sitting on platforms with wheels. One is a tree with a mass of 50 kg. It is moving at 3 m/s. The other is a fence with a mass of 30 kg. If the two set pieces have equal momentum, how fast is the fence moving?
momentum each= 50*3=30*v solve for v.
150
To determine the speed of the fence, we can use the principle of conservation of momentum. The principle states that the total momentum before an event is equal to the total momentum after the event, assuming no external forces are acting.
In this case, we have two set pieces with different masses, moving at different speeds. The tree has a mass of 50 kg and is moving at 3 m/s, while the fence has a mass of 30 kg, and we need to find its speed.
Let's set up some variables:
- The mass of the tree, m1 = 50 kg
- The speed of the tree, v1 = 3 m/s
- The mass of the fence, m2 = 30 kg
- The speed of the fence, v2 (what we need to find)
According to the conservation of momentum principle, the total momentum before the event (the moment when the set pieces have equal momentum) is equal to the total momentum after the event.
The momentum of an object can be calculated by multiplying its mass by its velocity. So we can write the equation for conservation of momentum as follows:
m1 * v1 = m2 * v2
Now, we just need to solve this equation for v2 (the speed of the fence). Let's plug in the given values:
50 kg * 3 m/s = 30 kg * v2
150 kg m/s = 30 kg * v2
Now, divide both sides of the equation by 30 kg to isolate v2:
v2 = 150 kg m/s / 30 kg
Simplifying the expression:
v2 = 5 m/s
Therefore, the fence is moving at a speed of 5 m/s.