"an ice cube of mass 50.0 g can slide without friction up and down a 25.0 degree slope. the ice cube is pressed against a spring at the bottom of the slope, compressing the spring 0.100 m . the spring constant is 25.0 n/m . when the ice cube is released, how far will it travel up the slope before reversing direction?"

The elastic potential energy is equal to the gravitational potential energy
If we set 0 GPE at max spring compression, then
total E = U = ½kx² = ½ * 25N / m * (0.1m) ² = 0.125 J
At max height,
GPE = 0.125 J = mgh = 0.05kg * 9.8m / s² * h
h = 0.255 m
Along the slope, that's a distance of
d = 0.255m / sin25º
d = 0.604 m
It's possible they want the distance from the end of the spring - that's 0.504 m

Answer Link

johanrusli johanrusli · Answer 2 · 2019-12-28T08:06:05+01:00

It will travel up the slope as far as about 0.604 m before reversing direction

[tex]\texttt{ }[/tex]

Further explanation

Let's recall Elastic Potential Energy formula as follows:

[tex]\boxed{E_p = \frac{1}{2}k x^2}[/tex]

where:

Ep = elastic potential energy ( J )

k = spring constant ( N/m )

x = spring extension ( compression ) ( m )

Let us now tackle the problem!

[tex]\texttt{ }[/tex]

Given:

mass of ice cube = m = 50.0 g = 0.05 kg

angle of slope = θ = 25.0°

compression of the spring = x = 0.100 m

spring constant = k = 25.0 N/m

Asked:

distance traveled = d = ?

Solution:

We will use Conservation of Energy formula to solve this problem:

[tex]\texttt{Elastic Potential Energy = Gravitational Potential Energy}[/tex]

[tex]\frac{1}{2}k x^2 = m g h[/tex]

[tex]\frac{1}{2}k x^2 = m g d \sin \theta[/tex]

[tex]d = (\frac{1}{2}k x^2) \div (mg \sin \theta)[/tex]

[tex]d = (\frac{1}{2} \times 25 \times 0.100^2) \div ( 0.05 \times 9.8 \times \sin 25.0^o)[/tex]

[tex]d \approx 0.604 \texttt{ m}[/tex]

[tex]\texttt{ }[/tex]

Learn more

Kinetic Energy : https://brainly.com/question/692781

Acceleration : https://brainly.com/question/2283922

The Speed of Car : https://brainly.com/question/568302
Young Modulus : https://brainly.com/question/9202964
Simple Harmonic Motion : https://brainly.com/question/12069840

[tex]\texttt{ }[/tex]

Answer details

Grade: High School

Subject: Physics

Chapter: Elasticity