Two blocks of masses m and M [M = 4.23m]
are placed on a horizontal, frictionless surface.
A light spring is attached to one of them, and
the blocks are pushed together with the spring
between them. A cord holding them together
is burned, after which the block of mass M
moves to the right with a speed of 2.35 m/s.
What is the speed of the block of mass m?
Answer in units of m/s.
[M = 4.23m]
makes no sense.
Mass is not measured in meters.
In a frictionless situation, total momentum is conserved.
multiple M and the velocity
9.9405
Answering to drwls late, but 4.23m, the m is mass of m but it's 4.23 times greater. Hence, 4.23m.
To find the speed of the block with mass m, we can use the principle of conservation of momentum. According to this principle, the total momentum before the cord is burned should be equal to the total momentum after the cord is burned.
Before the cord is burned, the two blocks are initially at rest and are pushed together with the spring between them. The system is at rest, so the initial momentum is zero.
After the cord is burned, only the block with mass M moves to the right with a speed of 2.35 m/s. The other block with mass m will also move, and we need to find its speed.
Let's denote the speed of the block with mass m as v. According to the conservation of momentum,
Initial momentum = Final momentum
0 = mv + M * 2.35
M = 4.23m
Substituting the value of M,
0 = mv + (4.23m) * 2.35
0 = mv + 9.9645m
Simplifying the equation,
mv = -9.9645m
Dividing both sides by m,
v = -9.9645
Therefore, the speed of the block with mass m is -9.9645 m/s.
Note: The negative sign indicates that the block is moving in the opposite direction to the block with mass M.