Question

Two objects of masses 1 kg and 3 kg are held stationary on a frictionless surface with a compressed massless spring between them. When the blocks are released, the 1 kg object moves to the left with velocity 9 m/s. What is the velocity with which the 3kg object moves to the right. Two blocks with masses 0.432 kg (A) and 0.834 kg (B) sit on a frictionless surface. Between them is a spring with spring constant 26.5 N/m, which is not attached to either block The two blocks are pushed together, compressing the spring by 0.302 meter, after which the system is released from rest. What is the final speed of the block A? Hint: you will need to use both conservation of energy and conservation of momentum to solve this problem).

Answer 1

The 3 kg object will move to the right with a velocity of 3 m/s, derived using the law of conservation of momentum.

Step-by-step explanation:

The initial scenario involves two objects with different masses on a frictionless surface separated by a compressed spring. Conservation of momentum dictates that the momentum before and after the release of the spring is the same because there are no external forces. Let's denote the mass of the first object as m1 with a value of 1 kg and its velocity as v1. The second object has a mass m2 of 3 kg and an unknown velocity v2.

Using the law of conservation of momentum:

m1 × v1 + m2 × v2 = 0

Where the initial momentum is zero because the system is initially at rest. After rearranging the formula to solve for v2, the following calculation can be made:

v2 = - (m1 × v1) / m2

After plugging in the values:

v2 = - (1 kg × 9 m/s) / 3 kg

We find that v2 = -3 m/s. The negative sign indicates that the direction of v2 is opposite to v1; since we declared v1 as to the left, v2 is then to the right.

Therefore, the 3 kg object moves to the right with a velocity of 3 m/s.

Answer 2

The 3 kg object will move with a velocity of 3 m/s due to conservation of momentum. To find the final speed of a block attached to a compressed spring, we apply the conservation of energy principle, where the potential energy in the spring is converted into the kinetic energy of the block.

Step-by-step explanation:

The student's question involves understanding the conservation of momentum and conservation of energy in the context of objects interacting with a spring on a frictionless surface. The first part of the question deals with determining the velocity of a 3 kg object when a 1 kg object is released with a velocity of 9 m/s. According to the law of conservation of momentum, the 3 kg object will move to the right with a velocity of 3 m/s since the total momentum before release is equal to the total momentum after release. The second part of the question requires us to find the final speed of a block attached to a compressed spring once the system is released. We utilize the conservation of energy principle to determine that the potential energy stored in the compressed spring will be completely converted to the kinetic energy of the block, giving us the final speed.