A box is initially at rest on an inclined plane tilted at angle theta with respe
ID: 1408853 • Letter: A
Question
A box is initially at rest on an inclined plane tilted at angle theta with respect to the horizontal. The box is attached by a low-mass, non-stretching rope to a freely-hanging mass. A uniform gravitational field (g) acts vertically downwards. The pulley is low-mass and frictionless. Given the information below:
theta = 29 degrees; mass of hanging = 3.74 kg; mass of box = 2.86 kg; coefficient of kinetic friction = 0.3; coefficient of static friction = 0.356
A. How much static friction is required to prevent the system from accelerating? What direction is the friction?
B. What is the maximum possible static friction?
C. Will the system accelerate when released from rest?
D. If it does accelerate:
what is the kinetic friction (magnitude and direaction), and what is the acceleration (magnitude and direction)?
E. What is the magnitude of the tension in the rope?
Explanation / Answer
A)
static friction required
f = 3.74x9.8 - ( 2.86x9.8sin29 )
f = 23.063 N
B)
fmax = us x 2.86x9.8xcos29
fmax = 8.727N
C)
it wii accelerate
D)
kinetic friction
fk = 0.3x2.86x9.8cos29 = 7.354 N ( down the incline
acceleration
a = 3.74x9.8 -fk-2.86x9.8xsin29 /3.74+2.86
a = 2.38 m/s^2 up the incline
E)
3.74x9.8 - T = 3.74xa
T = 3.74x9.8 - 8.9
T = 27.752 N
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