HW5 Chapter 5
38. In a circus performance, a monkey is strapped to a sled and both are given an initial speed of 4.0 m/s up a 20° inclined track. The combined mass of monkey and sled is 20 kg, and the coefficient of kinetic friction between sled and incline is 0.20. How far up the incline do the monkey and sled move? 5.38
Motion Diagram
Δx
Δt
Δv
a=
Δt
Δx = vi t + 12 at 2
v=
a
v
x=
t=
v=0
x=0
t=0
v=4 m/s
The FBD:
Ns,g
N − Wy = 0
N = Wy
fs,g
W y = mg cos 20°
− f − Wx = ma x
Ws,e
Wx = mg sin 20°
f sg = .2 N sg
Solve for W first then use that to get N.
Find friction using N and solve for a.
After finding a go back to the motion equations and solve for delta t with eq. 2.
x = 1.5 m
Now you can solve for final
Now solving by using the energy equation
K i − W f = PE g
1
2
mv 2 − fΔx = mgh
1
2
mv 2 − fΔx = mg (Δx sin 20°)
You know f from the FBD so the only unknown is delta x.
52. A block of mass 12.0 kg slides from rest down a frictionless 35.0° incline and is stopped by a strong spring with k = 3.00 × 104 N/m. The block slides 3.00 m from the point of release to the point where it comes to rest against the spring. When the block comes to rest, how far has the spring been compressed? 5.52
Choose PE g = 0 at the level where the block comes to rest against the spring. Then, in
the absence of work done by non-conservative forces, the conservation of mechanical
energy gives
( KE + PE
or
g
+ PEs ) = ( KE + PE g + PEs )
f
i
1
0 + 0 + kx 2f = 0 + mg L sin θ + 0 . Thus,
2
xf =
2 mg L sin θ
=
k
2 (12.0 kg ) ( 9.80 m s2 ) ( 3.00 m ) sin 35.0°
3.00 × 104 N m
= 0.116 m