Solving Blocks and Springs on a 15m Ledge: Energy, Velocity, Distance

In summary, the conversation discusses a scenario in which a 3 kg block is compressed 0.5 m by a spring with a spring constant of 15 N/m on a ledge 15 m above the ground. The block then falls vertically to the ground and rolls a distance D. The summary includes finding the initial elastic potential energy, initial gravitational potential energy, gravitational potential energy as the block hits the ground, block's velocity before hitting the ground, and D.
  • #1
Soaring Crane
469
0
There is a spring on a ledge that is 15 m above the ground. It is compressed 0.5 m by a block of 3 kg, and its spring constant is 15 N/m. I'm not certain of the exact wording, but somehow the compressed string (with the block) is the horizontal length of the ledge.

Now in this scenario, the block as a result of the spring falls from the ledge "vertically" to the ground and then rolls a distance D from the base of the ledge.

a. Find the initial elastic potential energy.

b. Find the initial gravitational potential energy of the block.

c. Find the gravitational potential energy of the block as it hits the ground.

d. Find the block's velocity before hitting the ground.

e. Find D.


Diagram:


/\/\/\/\|_|
------------
________|
________|
________|15 m
________|_______D_______

/\/\spring
|__|block


Any hints or pointers, aside from general formulas like kx^2/2 and and mgh, are appreciated.
 
Last edited:
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  • #2
You're going to have to show us what you did. It's hard to pick out where you are having trouble if we don't know what you did. Part (a) looks like you just have to take the numbers you are given and plug them into a formula.
 
  • #3
a. 1.875 J
b. 75 J
c. 0 J
d. 2.7 m/s
e. 4.7 m
 

FAQ: Solving Blocks and Springs on a 15m Ledge: Energy, Velocity, Distance

What is the equation for calculating the energy of a block on a spring?

The equation for calculating the energy of a block on a spring is E = 0.5kx², where E is the energy (in joules), k is the spring constant (in newtons per meter), and x is the distance the block is compressed or stretched (in meters).

How do you find the velocity of a block on a spring when it is released from a 15m ledge?

To find the velocity of a block on a spring when it is released from a 15m ledge, you can use the equation v = √(2gh), where v is the velocity (in meters per second), g is the acceleration due to gravity (9.8 m/s²), and h is the height of the ledge (15m).

What is the maximum distance a block on a spring can travel when released from a 15m ledge?

The maximum distance a block on a spring can travel when released from a 15m ledge is equal to the amplitude of the oscillation, which is given by A = √(2E/k), where A is the amplitude (in meters), E is the energy (in joules), and k is the spring constant (in newtons per meter).

How does the mass of the block affect the energy, velocity, and distance traveled on a 15m ledge?

The mass of the block does not affect the energy, velocity, and distance traveled on a 15m ledge as long as the spring constant and height of the ledge remain constant. These quantities are only dependent on the spring constant and the height of the ledge.

Can the energy, velocity, and distance of the block on a spring be calculated if the spring is not ideal?

Yes, the energy, velocity, and distance of the block on a spring can still be calculated even if the spring is not ideal. However, in this case, the spring constant will need to be determined experimentally rather than being given a specific value. Additionally, the energy will also be slightly less than the calculated value due to energy loss in the non-ideal spring.

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