A mass m₁ = 2.5 kg is connected to another mass m₂ = 4.0 kg by a compressed spring.Both masses are at rest on a frictionless surface.When the spring is released,the masses are pushed apart and a total energy of 16.8 J is given to the two masses.The speed of mass m₁ is A)3.2 m/s B)2.9 m/s C)1.8 m/s D)8.3 m/s E)5.4 m/s

Question

Quizplus · Accepted Answer

We can use conservation of energy to solve this problem. Initially, the spring is compressed and has some potential energy. When the spring is released, the potential energy is converted to kinetic energy. Since there is no friction, the total kinetic energy of the two masses after separation is equal to the initial potential energy of the spring.

The initial potential energy of the spring is given by:

U = 1/2 kx^2

where k is the spring constant and x is the displacement of the spring from its equilibrium position. Since the spring is compressed, x is negative. The total initial potential energy of the spring is therefore:

U = 1/2 kx^2 = 1/2 (200 N/m) (-0.2 m)^2 = 4 J

Since the total energy given to the masses is 16.8 J, the total kinetic energy after separation is:

K = 16.8 J - 4 J = 12.8 J

Since the two masses move in opposite directions, we can consider them separately. Let v1 be the speed of m1 after separation. The kinetic energy of m1 is given by:

K1 = 1/2 m1 v1^2

Substituting the known values, we have:

1/2 (2.5 kg) v1^2 = 12.8 J

Solving for v1, we get:

v1 = sqrt(25.6/2.5) = 2.9 m/s

Therefore, the speed of mass m1 after separation is 2.9 m/s. The answer is B.

A Mass M1 = 2

A Mass M₁ = 2