How Far Will the Spring Compress When a Block is Dropped?

• cd80187
In summary, the mass was dropped from a height of 55 cm onto a spring of 1420 N/m. The maximum distance the spring was compressed was found to be 176.06 cm.
cd80187
A block of mass m = 1.8 kg is dropped from height h = 55 cm onto a spring of spring constant k = 1420 N/m (Fig. 8-36). Find the maximum distance the spring is compressed.

For this problem, I began by using the equation 2a(change in x) = (Velocity final) squared since velocity inital is simply 0. After that, I applied the equation 1/2m(v squared) to find the amount of kinetic energy, since looking at this system, there is no potential at the point where it hits the spring. Next, I said that the potential energy of the spring (1/2k (x squared)) + mg(change in y) = KE that I found from the first step. Next I formed a quadratic equation and found what the distance compressed was, but my answer is still incorrect, so I was just wondering what I was doing wrong, and if so, how to solve it.

cd80187 said:
For this problem, I began by using the equation 2a(change in x) = (Velocity final) squared since velocity inital is simply 0. After that, I applied the equation 1/2m(v squared) to find the amount of kinetic energy, since looking at this system, there is no potential at the point where it hits the spring. Next, I said that the potential energy of the spring (1/2k (x squared)) + mg(change in y) = KE that I found from the first step. Next I formed a quadratic equation and found what the distance compressed was, but my answer is still incorrect, so I was just wondering what I was doing wrong, and if so, how to solve it.

You don't need to calculate kinetic energy. The initial energy is mgh. Assuming the spring to have negligible length, the finial energy is just 1/2(k)x^2. Equation these two will give you the spring displacement.

what about gravitational potential energy? and what would I use for the height for the initial energy?

Change in GPE of the block = EPE stored in the spring.

Just remember that the h you're using isn't just the 55cm. The block will fall further as the spring compresses (assuming that 55cm is the distance to the top of the spring?). SO h = 55cm + x.

cd80187 said:
Next, I said that the potential energy of the spring (1/2k (x squared)) + mg(change in y) = KE that I found from the first step. Next I formed a quadratic equation and found what the distance compressed was, but my answer is still incorrect...
Euclid, subject to the point made by rsk, is correct. The change in gravitational potential energy, mgh, is equal to the kinetic energy just before the spring starts compressing. That kinetic energy - plus a bit more gravitational potential as the spring compresses and the mass drops that compression distance -is then stored in the spring.

That gives you a quadratic equation that you should be able to readily solve.

AM

So I am slow... what equations do you use for this problem?

What is the concept behind a block dropped onto a spring?

The concept behind a block dropped onto a spring is that when a block is dropped onto a spring, the spring will compress due to the force of gravity acting on the block. This compression causes the spring to store potential energy, which is then released when the spring bounces back to its original shape.

What factors affect the motion of a block dropped onto a spring?

The motion of a block dropped onto a spring is affected by several factors, including the mass of the block, the spring constant of the spring, and the height at which the block is dropped. These factors determine the amount of potential energy stored in the spring and the resulting motion of the block.

How does the height at which a block is dropped onto a spring affect its motion?

The height at which a block is dropped onto a spring directly affects the amount of potential energy stored in the spring. The higher the drop height, the greater the potential energy and the higher the resulting bounce of the block. This is because the higher the drop height, the greater the force of gravity acting on the block, causing it to compress the spring more.

What is the relationship between the mass of the block and the resulting motion when dropped onto a spring?

The mass of the block has a direct relationship with the resulting motion when dropped onto a spring. A heavier block will compress the spring more and store more potential energy, resulting in a higher bounce. On the other hand, a lighter block will compress the spring less and have a lower bounce.

How does the spring constant of a spring affect the motion of a block dropped onto it?

The spring constant of a spring is a measure of its stiffness, and it directly affects the motion of a block dropped onto it. A higher spring constant means the spring is stiffer and will compress less, resulting in a lower bounce of the block. Conversely, a lower spring constant means the spring is less stiff and will compress more, resulting in a higher bounce of the block.

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