On the smooth horizontal plane, there is a wooden board with L = 4m and M = 3kg mass (excluding thickness), and a small object with M = 1kg mass is placed on the rightmost side of the board The dynamic friction coefficient between M and M is u = 0.1. Now, a horizontal right pulling force F.G = 10m / s ＾ 2 is applied to the board. Find (1) how much f can't exceed in order to prevent the small object from sliding relative to the board? (2) if the pulling force F = 10N, how long does it take for the small object to fall off the board?

On the smooth horizontal plane, there is a wooden board with L = 4m and M = 3kg mass (excluding thickness), and a small object with M = 1kg mass is placed on the rightmost side of the board The dynamic friction coefficient between M and M is u = 0.1. Now, a horizontal right pulling force F.G = 10m / s ＾ 2 is applied to the board. Find (1) how much f can't exceed in order to prevent the small object from sliding relative to the board? (2) if the pulling force F = 10N, how long does it take for the small object to fall off the board?

When there is no relative sliding between the small object and the board, the small object and the board accelerate together: F = (M + m) a
Small objects were analyzed separately: F > MA, that is: μ mg > MA, a < μ G
∴F=(M+m)＜μ(M+m)g=0.1*（3+1）*10=4N
That is, f cannot exceed 4N
If the tensile force F = 10N:
The acceleration of small objects produced by dynamic friction: F = MA1, μ mg = MA1, A1 = μ g = 0.1 * 10 = 1m / S ^ 2
Analysis results: f-f = ma2, F - μ mg = ma2
a2=(F-μmg)/M=(10-0.1*1*10)/3=3m/s^2
X2-x1 = L = 4m
1/2a2t^2-1/2a1t^2=4
T = radical [2 * 4 / (a2-a1)] = radical [8 / (3-1)] = 2S
The time of pulling force F is at least 2 s