Mastering Physics Solutions: Two Blocks and a Pulley

Mastering Physics Solutions: Two Blocks and a Pulley

On February 9, 2014, in Chapter 04: Force and Motion, by Mastering Physics Solutions

Two Blocks and a Pulley

Part A = (a + gsin(θ) + μgcos(θ)) / (g – a)

Solution Below:

Block 1, of mass m1 = 0.650 kg , is connected over an ideal (massless and frictionless) pulley to block 2, of mass m2, as shown. For an angle of θ = 30.0° and a coefficient of kinetic friction between block 2 and the plane of μ = 0.200, an acceleration of magnitude a = 0.450m/s2 is observed for block 2.

Part A

Find the mass of block 2, m2.

There are a couple ways to solve this problem. One method is to have a look at the problem Two Masses a Pulley and an Inclined Plane. The problem linked gives you a formula to find the ratio of the masses m1 and m2. This formula is:

m1/m2 = (a + gsin(θ) + μgcos(θ)) / (g – a)

This gives us:

0.650/m2 = ((0.450 + 9.8 * sin(30)) + (0.200 * 9.8 * cos(30))) / (9.8 – 0.450)
0.650/m2 = (2.205 + 1.70) / (9.350)
0.650/m2 = 0.4176
0.650 = 0.4176m2
m2 = 1.56 kg

1.56 kg

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