How Far Will the Ice Cube Travel Up the Slope?

In summary, an ice cube weighing 55g can slide up and down a 25º slope without any friction. When pressed against a spring at the bottom of the slope, the spring is compressed by 10cm with a spring constant of 25N/m. Using the equations for elastic potential energy and gravitational potential energy, the maximum height that the ice cube can reach is 0.23m or 23cm. However, the question asks for the distance traveled along the slope, which can be calculated by multiplying the maximum height by the sine of the slope angle, resulting in a distance of 0.4m or 40cm.
  • #1
Ritzycat
171
4
Question statement
A 55g ice cube can slide without friction up and down a 25∘slope. The ice cube is pressed against a spring at the bottom of the slope, compressing the spring 10cm . The spring constant is 25N/m. When the ice cube is released, what distance will it travel up the slope before reversing direction?

Relevant equations
[itex]PE_s = PE_g[/itex]
[itex]PE_s = 1/2kx^2[/itex]
[itex]PE_g = mgh[/itex]

Attempt at a solution
Maximum height is when all energy is converted to gravitational potential energy (frictionless environment)

Thus,

[itex]PE_s = PE_g[/itex]

[itex]1/2kx^2 = mgh[/itex]

[itex]1/2(25N/m)(0.1m)^2 = (0.055kg)(9.8m/s^2)(h)[/itex]

[itex]h = 0.23m[/itex] or [itex] 23 cm[/itex]
(Answer is asked for in cm)

Not sure what I am doing wrong here...
 
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  • #2
You computing the height, not the distance along the slope.
 
  • #3
I'm so silly. I need to learn to read questions further before answering something different.

Distance up slope would be
[itex]0.23(sin 35°) = 0.40m = 40cm[/itex]

but that's not right!

How do I compute the distance up the slope?
 
  • #4
Wasn't it a 25º slope?
 
  • #5
Yes, it was... Thanks...

:nb)
 

Related to How Far Will the Ice Cube Travel Up the Slope?

1. How does an ice cube go up a ramp?

An ice cube goes up a ramp due to the force of gravity. The ramp is inclined at an angle, causing the ice cube to move upwards as it slides down the ramp. The friction between the ice cube and the ramp helps to slow down the ice cube's descent, allowing it to travel up the ramp.

2. Why does an ice cube go up a ramp?

An ice cube goes up a ramp because of the laws of physics. Gravity pulls objects towards the center of the Earth, and the inclined ramp provides a surface for the ice cube to slide on. The angle of the ramp influences how fast the ice cube will go up the ramp.

3. What factors affect how an ice cube goes up a ramp?

The angle of the ramp, the force of gravity, and the friction between the ice cube and the ramp are all factors that affect how an ice cube goes up a ramp. The weight and size of the ice cube may also play a role in its movement up the ramp.

4. Can an ice cube go up a ramp without any friction?

No, an ice cube cannot go up a ramp without any friction. Friction is necessary to slow down the ice cube's descent and allow it to travel up the ramp. Without friction, the ice cube would simply slide down the ramp without going up.

5. Is it possible for an ice cube to go up a ramp without any force applied?

Yes, it is possible for an ice cube to go up a ramp without any force applied. As long as the ramp is inclined at an angle and there is friction between the ice cube and the ramp, the ice cube will move up the ramp due to the force of gravity.

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