Calculating Maximum Height and Final Velocity: 2 Energy Problems on a Slope

In summary, for the first conversation, a 50g ice cube with no friction compresses a string with a constant of 25 N/m a total of 10 cm. The maximum height reached by the ice cube before it starts sliding back down the slope is 0.255m. And for the second conversation, a cannon angled at 30 degrees above the horizontal launches a cannonball at 80 m/s. If the cannon is 10 m above the ground, the speed at which the cannonball strikes the ground is 81.216 m/s.
  • #1
rain_ex
6
0

Homework Statement



A 50g ice cube has no friction. It compresses a string with the constant 25 N*m a total of 10 cm. Find the max height reached by the ice cube before it starts sliding back down the slope, after it is released from the spring.

Known:
m = 50g (.05kg)
k = 25 Nm
x = 10cm (.1m)

Homework Equations



E0 = E <- general
Us0 = Ug <- expanded
1/2kx2 = mgh <- final equation

The Attempt at a Solution



I ended up with 0.255m. Is this correct? I solved for the variable "h".

Homework Statement



A cannon angled 30 degrees above the horizontal launches a cannanball at 80 m/s. if the cannon is 10 m above the ground with what speed does the cannon ball strike the ground?

Homework Equations




E0 = E <- general
Ug0 + K0 = K <- expanded
mgh+1/2mv02 = 1/2mv2 <-final equation

The Attempt at a Solution



I ended up with 81.216 m/s. I solved for the variable "v".

Please check my solutions for me! Thank you!
 
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  • #2
Your solution is correct, but the unit of the spring constant k is N/m instead of Nm.

ehild
 
  • #3
Thank you.
I'm assuming that the 2nd question's solution was correct too?
 
  • #4
Yes, both solutions are correct.

ehild
 
  • #5




Your solutions appear to be correct. In the first problem, you correctly used the conservation of energy equation to solve for the maximum height reached by the ice cube. In the second problem, you used the conservation of energy equation again, taking into account the initial potential and kinetic energies to solve for the final velocity of the cannonball before it strikes the ground. Overall, your approach and solutions demonstrate a good understanding of energy conservation principles. Keep up the good work!
 

FAQ: Calculating Maximum Height and Final Velocity: 2 Energy Problems on a Slope

1. What are the two problems on energy?

The two problems on energy are the depletion of non-renewable energy sources and the negative environmental impacts of energy production and consumption.

2. How does the depletion of non-renewable energy sources affect us?

The depletion of non-renewable energy sources, such as fossil fuels, can lead to energy shortages and price increases. It also contributes to climate change and air pollution.

3. What are the negative environmental impacts of energy production and consumption?

The negative environmental impacts of energy production and consumption include air and water pollution, deforestation, and greenhouse gas emissions, which contribute to climate change and global warming.

4. How can we address these problems on energy?

We can address these problems by transitioning to renewable energy sources, such as solar and wind power, and implementing energy efficiency measures. We can also reduce our overall energy consumption and promote sustainable practices.

5. What role do individuals play in solving these problems?

Individuals play a crucial role in solving these problems by making sustainable choices in their daily lives, such as using public transportation, conserving energy at home, and supporting renewable energy initiatives. They can also advocate for government policies and regulations that promote sustainable energy practices.

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