A 4.5 kg box slides down a 5.1-m-high frictionless hill, starting from rest, acr
ID: 2016593 • Letter: A
Question
A 4.5 kg box slides down a 5.1-m-high frictionless hill, starting from rest, across a 1.7-m-wide horizontal surface, then hits a horizontal spring with spring constant 530 N/m. The other end of the spring is anchored against a wall. The ground under the spring is frictionless, but the 1.7-m-long horizontal surface is rough. The coefficient of kinetic friction of the box on this surface is 0.27. What is the speed of the box just before reaching the rough surface? Express your answer using two significant figures. What is the speed of the box just before hitting the spring? Express your answer using two significant figures. How far is the spring compressed? Express your answer using two significant figures. Including the first crossing, how many complete trips will the box make across the rough surface before coming to rest?Explanation / Answer
m = 4.5 kg, h = 5.1 m, s = 7.1 m, k = 530 N/m, = 0.27
(A) Conservation of energy: m g h = (1/2) m v12
v1 = (2 g h)
(B) Work-energy theorem. Remember that friction does negative work: W = E
-f s = (1/2)m v22 - (1/2) m v12
- n s = (1/2)m v22 - (1/2) m v12
- m g s = (1/2)m v22 - (1/2) m v12
v2 = (v12-2gs)
(C) Again, conservation of energy: (1/2)m v22 = (1/2) k x2
x = v2(m/k)
(D) Again, the work energy theorem. Initially, the box has no kinetic energy and gravitational energy equal to m g h. At the end, the box has no energy whatsoever (it's at ground level and it's not moving).
W = E
-f Ns = 0 - m g h
N = m g h/(f s) = m g h/( m g s) = h/( s)
When you plug in the numbers for this, you'll find it simplifies, since 5.1 = 3 x 1.7
N = 5.1/(0.27 x 1.7) = 100/9 = 11.111..., or 11 complete trips. Unless a complete trip is from the base of the hill and back again, in which case N = (100/9)/2 = 50/9 = 5.555..., or 5 complete trips.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.