Question

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?Identify the initial and final gravitational potential energies.Enter your answers, separated by a comma, in terms of some or all of the variables m, k, x, d, θ, and the acceleration due to gravity, g.Identify the initial and final elastic potential energies.Enter your answers, separated by a comma, in terms of some or all of the variables m, k, x, d, θ, and the acceleration due to gravity, g.

Answer 1

The initial gravitational potential energy of the ice cube is zero, and the final gravitational potential energy is mgxsin(θ). The initial elastic potential energy of the spring is 0.125 J, and the final elastic potential energy is zero.

Step-by-step explanation:

First, let's calculate the initial gravitational potential energy of the ice cube. The potential energy is given by the formula PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. Since the ice cube is at the bottom of the slope, the height h is zero. Therefore, the initial gravitational potential energy is 0.

Next, let's calculate the final gravitational potential energy of the ice cube. When the ice cube reaches the maximum height before reversing direction, its height h is given by h = d * sin(θ), where d is the distance traveled up the slope and θ is the angle of the slope. Plugging in the values, we get h = x * sin(θ). Therefore, the final gravitational potential energy is mgh = mgxsin(θ).

The initial elastic potential energy of the spring is given by the formula PE = 0.5kx^2, where k is the spring constant and x is the compression distance. Plugging in the values, we get PE = 0.5 * 25.0 * (0.100)^2 = 0.125 J. The final elastic potential energy is zero because the spring is fully extended when the ice cube reaches the maximum height.