two 10-kg boxes are connected by a massless string that passes over a massless f
ID: 1408578 • Letter: T
Question
two 10-kg boxes are connected by a massless string that passes over a massless frictionless pulley as shown above. The boxes remain at rest, with the one on the right hanging vertically and the one on the left d = 2.0 m from the bottom of an inclined plane that makes an angle of theta = 60degree with the horizontal. The coefficients of kinetic friction and static friction between the left land box and the plane are 0.15 and 0.30 respectively.
a. what is the tension on the string
b. Determine the magnitude of the frictional force acting on the box and the plane.
c. The string is then cut and the left-hand box slide-down the inclined plane. Determine the acceleration of each block
d. suppose thers is a spring with spring constant k=10N/m at the bottom of the ramp. How much will the spring compress when the block comes to rest?
Explanation / Answer
a) for hanging block,
T = mg = 10 x 9.8 = 98 N
b) along the incline,
T - mgsin@ - f = 0
98 - (10 x 9.8 x sin60) - f = 0
f = 13.13 N
c) for hanging block, (it is in free fall)
a = g = 9.8 m/s^2
for block on incline,
N = mgcos60
f = uk N = 0.15 mgcos60
so mgsin60 - 0.15mgcos60 = ma
a = 7.75 m/s^2
d) Fnet along the incline,
F = ma = 10 x 7.75 = 77.5 N
using energy conservation,
work done by force = spring potentail energy
77.5 * (2+ x) = 10x^2 /2
5x^2 - 77.5x - 155 =0
x = 17.3 m
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