A box with mass m = 2 kg initially compresses a spring with spring constant k = 100 N by a displacement Ars. The mass is released and it travels to the right through a rough patch with = 0.1, length Ax, = 2, and up a frictionless slope at an incline angle = 45°. The mass comes to a momentary stop after it has traveled 10 meters up the slope on the right. (m ΔΧ, Figure 3: Diagram of the problem What is the box's speed before and after the rough patch? 6 By how much does the box + rough patch have its thermal energy increased after the box slides over the rough patch? What is the instantaneous rate at which the box loses energy to the rough patch the moment it enters the rough patch? What is the initial spring displacement Axs?
A box with mass m = 2 kg initially compresses a spring with spring constant k = 100 N
by a displacement ∆xs. The mass is released and it travels to the right through a rough patch with μk
= 0.1, length ∆xr = 2, and up a frictionless slope at an incline angle φ = 45◦. The mass comes to a
momentary stop after it has traveled 10 meters up the slope on the right. (Diagram attached in image)
A) What is the box’s speed before and after the rough patch?
B) By how much does the box + rough patch have its thermal energy increased after the
box slides over the rough patch? What is the instantaneous rate at which the box loses energy to the
rough patch the moment it enters the rough patch?
C) What is the initial spring displacement ∆xs?
D) Calculate the total mechanical energy of the system when the box is at its maximum
height on the slope, and when the box is initially compressing the spring by the maximum amount ∆xs.
What causes the difference in these two values?
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