# Block moved by spring - Determine speed

• starfish794
In summary, the problem involves a 2.5 kg block attached to a horizontal spring with a constant of 19.6 N/m. A horizontal force of 20 N is applied, causing the spring to stretch. To determine the speed of the block after it has moved 0.900 m from equilibrium, the formula v= square root of k/m*(A^2-x^2) was used, but resulted in the wrong answer. The 20 N force must be included in the problem in some way. The problem is further complicated by unclear wording. A hint is given to use the work of the force and the spring's potential energy to calculate the stretch of the spring and use energy conservation to solve the problem.
starfish794
A 2.5 kg block at rest on a tabletop is attached to a horizontal spring having constant 19.6 N/m. The spring is initially unstretched. A constant 20 N horizontal force is applied to the object, causing the spring to stretch. Determine the speed of the block after it has moved 0.900 m from equilibrium if the surface between the block and tabletop is frictionless.

I tried using the formula v= square root of k/m*(A^2-x^2) and got 2.52 which is the wrong answer. The 20 N force must need to be included in the problem in some way but I can't figure out how.

What exactly do you mean by '0.900 m from equilibrium'? Do you mean, the point at which the spring was unstreched?

That's what I took it to mean. I think the wording in the whole problem is bad.

starfish794 said:
That's what I took it to mean. I think the wording in the whole problem is bad.

Okay, here's a hint: use the fact that the work of the force along the unknown displacement (i.e. extension of the spring) equals the change of the spring's potential energy. You should be able to calculate the stretch of the spring from that equation. Further on, by knowing the initial displacement, use energy conservation.

## 1. How can the speed of a block moved by a spring be determined?

The speed of a block moved by a spring can be determined using the formula v = √(k/m) * A, where v is the speed, k is the spring constant, m is the mass of the block, and A is the amplitude of the spring's oscillation.

## 2. What factors affect the speed of a block moved by a spring?

The speed of a block moved by a spring is affected by the spring constant, mass of the block, and the amplitude of the spring's oscillation. A stiffer spring, lighter block, and larger amplitude will result in a higher speed.

## 3. Can the speed of a block moved by a spring change during its motion?

Yes, the speed of a block moved by a spring can change during its motion. As the spring oscillates, the speed of the block will also oscillate, reaching maximum speed at the equilibrium point and decreasing as it moves away from the equilibrium point.

## 4. Is the speed of a block moved by a spring affected by external forces?

Yes, the speed of a block moved by a spring can be affected by external forces such as friction or air resistance. These forces can slow down the movement of the block and decrease its speed.

## 5. How does the speed of a block moved by a spring relate to its potential and kinetic energy?

The speed of a block moved by a spring is directly related to its kinetic energy. As the block moves faster, its kinetic energy also increases. At the same time, the potential energy of the spring decreases as it returns to its equilibrium position.

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