1.a crate of mass m =39 kg rides on the bed of a truck attached by a cord to the

Question

        1.a crate of mass m =39 kg rides on the bed of a truck attached by a cord to the back of the cab  the cord can withstand a maximum tension of 6s N before breaking. Neglecting friction between the crate and truck bed, find the maximum acceleration the trucj can have before the cord breaks

        2. two blocks of masses m and 2m are held in equilibrium on frictionless incline  in terms of m and delta find

A) the magnitude of the tension T1 in the upper cord and B) the magnitude of the tension T2 in the lower cord connection the two blocks.

Explanation / Answer

1)Acceleration maximum = (force/ mass), = 65/39, = 1.6666m/sec^2

2)First, you need to draw your free body diagram for m and 2m. In this problem, you need to understand that T1 is not equal to T2, why ? because T1 and T2 is not on the same rope or string ;).

I wish I could upload my diagram here, but, anyway, this is what I did
Take upwards as positive, and x+ from left to right. The system is held in equilibrium, so acceleration should be equal to 0

For m:
y direction:
-mgcos theta + N1 = 0

x direction:
-T1 + mgsin theta + T2 = 0 (1)

For 2m
y direction:
-2mgcos theta + N2 = 0

x direction:
2mgsin theta - T2 = 0
T2 = 2mgsin theta

(1) ----------> T 1= mgsin theta + 2mgsin theta = 3mgsin theta

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