Mass falling on a vertical spring

In summary, a 195 g block is dropped onto a relaxed vertical spring with a spring constant of 1.6 N/cm. The block becomes attached to the spring and compresses it 14 cm before momentarily stopping. During the compression, the gravitational force does 0.26754 joules of work on the block, while the spring force does -1.568 joules of work. The speed of the block just before it hits the spring is 3.65212969 m/s (assuming negligible friction). If the speed at impact is doubled, the maximum compression of the spring can be calculated by considering the conversion of kinetic energy into potential energy in the spring. This can be done using the formula for potential energy in a spring
  • #1
bikerboi92
8
0
A 195 g block is dropped onto a relaxed vertical spring that has a spring constant of 1.6 N/cm. The block becomes attached to the spring and compresses the spring 14 cm before momentarily stopping.

(a) While the spring is being compressed, what work is done on the block by the gravitational force?

.26754 joules

(b) While the spring is being compressed, what work is done on the block by the spring force?

-1.568 joules

(c) What is the speed of the block just before it hits the spring? (Assume that friction is negligible.)

3.65212969 m/s

(d) If the speed at impact is doubled, what is the maximum compression of the spring?

This is the only part that I can not get
 
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  • #2
You can count the speed of the block at impact. You double it, which essentially gives a new value for its kinetic energy. This kinetic energy (and some potential energy as the spring is compressed, the block comes closer to the ground, i.e. it loses potential energy) is then transformed into potential energy in the spring. From that you can get the maximal compression.

Potential energy in spring=0.5kx^2

where k is the spring constant and x is the compression. Maybe that helps a little bit?
 
  • #3
I'm you didn't understand Ofey, its pretty simple really. You know that energy cannot be created or destroyed, only transferred. When a mass is dropped onto a spring, potential energy is converted to kinetic.
[tex] (mgz)_1 = \left(\frac{1}{2}m v^2\right)_2[/tex]
At the bottom of the fall, the kinetic energy is converted into potential energy in the spring.
[tex] \left(\frac{1}{2}m v^2\right)_1 = \left( \frac{1}{2}k z^2\right)_{spring}[/tex]
Keeping the z notation. The question is if V = 2V, find z.

*note for simplicity I have neglected potential energy conversion during the spring compression as Ofey mentioned. For complete accuracy, you should take into account (i.e. however this might be an iterative process since you don't know the compression beforehand).
 

Related to Mass falling on a vertical spring

What is the concept of mass falling on a vertical spring?

The concept of mass falling on a vertical spring involves the interaction between the force of gravity and the restoring force of a spring. As the mass falls onto the spring, it compresses the spring and creates potential energy. This potential energy is then converted into kinetic energy as the spring bounces back, causing the mass to bounce up and down.

What factors affect the motion of a mass falling on a vertical spring?

The motion of a mass falling on a vertical spring can be affected by several factors, such as the mass of the object, the stiffness of the spring, and the height from which the mass is dropped. The gravitational acceleration and air resistance can also play a role in the motion.

How does the mass of the object affect the motion of a mass falling on a vertical spring?

The mass of the object directly affects the amplitude and frequency of the motion of a mass falling on a vertical spring. A heavier mass will compress the spring more, resulting in a larger amplitude and slower frequency. On the other hand, a lighter mass will result in a smaller amplitude and faster frequency.

What is the significance of the spring constant in a mass-spring system?

The spring constant, also known as the stiffness constant, determines the amount of force required to compress or stretch a spring. In a mass-spring system, a higher spring constant will result in a stiffer spring, leading to a smaller amplitude and faster frequency of motion.

How does air resistance affect the motion of a mass falling on a vertical spring?

Air resistance can affect the motion of a mass falling on a vertical spring by slowing down the fall of the mass and reducing the amplitude of the bounces. This is because air resistance creates a drag force that acts against the motion of the mass, causing it to lose energy and decrease in amplitude over time.

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