關於DYNAMICS的簡單物理問題

Tieria

2010-10-08 3:06 am

1. A trolley of mass M = 3 kg is placed on a horizontal bench. A string attached to the trolley passes over a smooth light pulley placed at the edge of the bench. A mass m = 2 kg is hung at the end of the string. The system accelerates at 1 ms^-2. (a) What is the tension in the string?(b) What is the frictional force acting on the block?(c) What is the coefficient of kinetic friction between the block and the bench? 2. A block of mass m rests on the top of a trolley of mass M. The coefficient of friction between the block and the trolley is μ. What is the minimum force that must be applied to the trolley so that m will slip off the trolley? ※請列明計算步驟。※

回答 (1)

天同

2010-10-08 4:17 am

✔ 最佳答案

(a) Let T be the tension in the string. Apply force = mass x acceleration to the 2 kg mass, we have,
2g - T = 2 x1, where g is the acceleration due to gravity (taken to be 10 m/s2 for simplicity of calculation).
hence, T = (2g - 2) N = 18 N

(b) Consider the 3 kg mass,
T - Ff = 3 x 1, where Ff is the frictional force acting on the mass
i.e. Ff = (T - 3 ) N = (18-3) N = 15 N

(c) Coefficient of friction = 15/3g = 0.5

2. When a force is applied to the trolley, acceleration a of the trolley-and-block is,
F = (M+m).a
i.e. a = F/(M+m)

The block will be caught to accelerate with the trolley if the reaction of the frictional force between trolley-and-block can provide the necessary force. That is,
μmg = ma
i.e μmg = m[F/(M+m)]
hence, F = μ(M+m)g

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