Energy conservation of ice problem

In summary, a block of ice with a mass of 44 kg slides with negligible friction or air resistance on a curved path with a radius of curvature of 3.4 m. Its initial speed is 1.3 m/s and its height is 4.1 m. Using the equations for energy and circular motion, the force exerted by the path on the ice is calculated to be 630.8 N upwards, with a net force of 680.8 N. The common error of treating centripetal force as an applied force is noted.
  • #1
paulxu11
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Homework Statement


https://moodle.telt.unsw.edu.au/pluginfile.php/2296810/question/questiontext/2691158/6/1668509/cart%20track.png
A block of ice (that we shall treat as a particle) slides with negligible friction or air resistance on the curved tpath sketched (black line). The mass of the block is m = 44 kg. Its initial speed is v0 = 1.3 m.s–1. The height h= 4.1 m. At the bottom, the path has a radius of curvature (fine circle) R = 3.4 m. At the bottom of the path, what is the force exerted on the ice by the path?

Homework Equations


K + V = constant

The Attempt at a Solution


Energy before it slides = after it slides:
mgh + 1/2 * m*v0^2 = 1/2 * m*v_final^2 (at the bottom h = 0 -> mgh=0)
44*9.8*4.1 + 1/2*44*1.3^2 = 1/2*44*v_final^2 -> v_final=9.06m/s

Circular motion:
Fc=ma=m*v_f^2/R=44*9.06^2/3.4=1062N upwards
W=mg=44*9.8=431.2N downwards
F_path=1062-431.2=630.8N upwards

Could someone suggest where I did wrong?
Thanks!:smile:
 
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  • #2
The pic is here
Snip20170401_5.png
 
  • #3
paulxu11 said:
Circular motion:
Fc=ma=m*v_f^2/R=44*9.06^2/3.4=1062N upwards
W=mg=44*9.8=431.2N downwards
F_path=1062-431.2=630.8N upwards

Could someone suggest where I did wrong?

If W and F_path are in opposite directions, the magnitude of the net force is 680.8 N - 431.2 N, no?
 
  • #4
paulxu11 said:
06^2/3.4=1062N upwards
W=mg=44*9.8=431.2N downwards
F_path=1062-431.2=630.8N upwards
This is a very common error.
Centripetal force is not an applied force. It is that component of the resultant which is perpendicular to the velocity.
So in ΣF=ma, the centripetal force is the ma on the right, and the perpendicular component of each applied force appears in the sum on the left.
 
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1. How does energy conservation apply to melting ice?

Energy conservation is a fundamental law of physics that states energy cannot be created or destroyed, only transferred or converted into different forms. In the case of melting ice, the energy from the surrounding environment is transferred to the ice, causing its molecules to vibrate and break apart, resulting in a phase change from solid to liquid. This process is known as energy conservation of ice problem.

2. What factors affect the rate of ice melting?

Several factors can affect the rate of ice melting, including the temperature of the surrounding environment, the size and shape of the ice, and the presence of other substances such as salt or sugar. Additionally, the material of the container holding the ice can also impact the rate of melting, as some materials are better conductors of heat than others.

3. Can ice melt without any external energy input?

No, according to the law of energy conservation, energy must always be transferred or converted. Therefore, for ice to melt, it requires an external energy source, such as heat from the surrounding environment. However, the amount of energy needed may vary depending on the factors mentioned above.

4. How can we conserve energy while melting ice?

There are a few ways to conserve energy while melting ice. First, using materials that are better insulators, such as styrofoam or double-walled containers, can help slow down the melting process by reducing the transfer of heat from the environment. Additionally, using colder water or ice cubes can also decrease the amount of energy needed to melt the ice.

5. How does energy conservation of ice problem relate to climate change?

The concept of energy conservation of ice problem is crucial in understanding the effects of climate change on our planet. As temperatures rise due to increasing levels of greenhouse gases, more energy is transferred to the Earth's surface, resulting in the melting of ice in polar regions. This process not only contributes to rising sea levels but also has a cascading effect on various ecosystems and wildlife that depend on ice for survival.

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