A 4 kg block rests on a horizontal table, attached ... A 4 kg block rests on a h
ID: 1396075 • Letter: A
Question
A 4 kg block rests on a horizontal table, attached ...
A 4 kg block rests on a horizontal table, attached to a 2 kg block by a light string as shown in the figure. The acceleration of gravity is 9.81 m/s^2. What is the minimum coefficient of static friction such that the objects remain at rest? If the coefficient of static friction is less than that found above, and if the coefficient of kinetic friction between the block and the table is 0.4, find the time it takes for the 2 kg mass to fall 10 m to the floor if the system starts from rest. Answer in units of s.Explanation / Answer
For the 4 kg body, summing forces along y,
N - 4 g = 0
--> N = 4 g = 39.24 N
Summing forces along x for the 4 kg body,
us N - T = 0
Summing forces along y for the 2 kg body,
T - 2 g = 0
--> T = 19.62 N
Thus,
us N - T = 0
Plugging in N and T,
us = 0.500 [ANSWER]
*****************************
If uk = 0.4, then summing forces along x for the 4 kg body,
T - uk N = 4 a
where N = 39.24 N.
Summing forces along y for the 2 kg body,
2 g - T = 2 a
Adding these two equations to cancel T,
2g - uk N = 2a
Solving for a,
a = 1.962 m/s^2
Using
d = vo t + 1/2 a t^2
As vo = 0, solvin for t,
t = 3.193 s [ANSWER]