1. A light rope is attached to a block with mass 4.00 kg that rests on a frictio

Question

1. A light rope is attached to a block with mass 4.00 kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass m is suspended from the other end. When the blocks are released, the tension in the rope is 17.7 N .

A)Find m

2. A 538-N physics student stands on a bathroom scale in an 849-kg (including the student) elevator that is supported by a cable. As the elevator starts moving, the scale reads 448 N

A) The magnitude of the acceleration of the elevator is 1.64 m/s2 , what is the tension in the cable?

Explanation / Answer

1a.

T = m1*a
a = T/m1 = 17.7 / 4.00 = 4.425 m/sec^2

now Find the mass m .
a = 4.425 = mx*g/(m1+mx) =9.8mx/(4.00+mx)
17.7 + 4.425mx = 9.8mx
17.7 = 5.375 * mx
mx = 17.7 / 5.375 = 3.29 kg answer
check
motive force Fm = mx*g = 3.29*9.8 = 32.27 N
acceleration a = Fm/(m1+mx) = 32.27 / (4 + 3.29) = 4.42 m/s2

2.solution

Student's mass m = W / g = 538 N / 9.8m/s² = 54.89 kg
Scale reading F = 448 N = m(g + a) = 54.89kg(9.8m/s² + a)
a = -1.64 m/s² (that is, down)   

Tension = m(g + a) = 849 kg(9.8m/s² - 1.64m/s²) = 6927.84 N

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