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nika2105 [10]
3 years ago
11

A 12.0-kg package in a mail-sorting room slides 2.00 m down a chute that is inclined at 53.0° below the horizontal. The coeffici

ent of kinetic friction between the package and the chute’s surface is 0.40. Calculate the work done on the package by (a) friction, (b) gravity, and (c) the normal force. (d) What is the net work done on the package
Physics
1 answer:
zvonat [6]3 years ago
7 0

Answer

given,

mass of the package = 12 kg

slides down distance = 2 m

angle of inclination = 53.0°

coefficient of kinetic friction = 0.4

a) work done on the package by friction is

              W_f = -μk R d

                   = -μk (mg cos 53°)(2.0)

                   =-(0.4)(8.0 )(9.8)(cos 53°)(2.0)

                   = -37.75 J

b)

work done on the package by gravity is

             W_g = m (g sin 53°) d

                   = (8.0 )(9.8 )(sin 53°)(2.0 )

                   =125.23 J

c)

the work done on the package by the normal force is

             W_n = 0

d)

the net work done on the package is

           W = -37.75 + 125.23 + 0

           W = 87.84 J

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son4ous [18]

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The object accelerates downward at 4 m/s² since the tension on the rope is less than weight of the object.

Explanation:

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mass of the object, m = 2 kg

weigh of the object, W = 20 N

tension on the rope, T = 12 N

The acceleration of the object is calculated by applying Newton's second law of motion as follows;

T = F + W

T = ma + W

ma = T - W

a = \frac{T-W}{m} \\\\a = \frac{12 - 20}{2} \\\\a = -4 \ m/s^2 (the negative sign indicates deceleration of the object)

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7 0
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A force in the +x -direction with magnitude F(x)=18.0N−(0.530N/m)x is applied to a 7.90 kg box that is sitting on the horizontal
dsp73

Answer:

v\approx 8.570\,\frac{m}{s}

Explanation:

The equation of equlibrium for the box is:

\Sigma F_{x} = 18\,N-(0.530\,\frac{N}{m} )\cdot x = (7.90\,kg)\cdot a

The formula for the acceleration, given in \frac{m}{s^{2}}, is:

a = \frac{18\,N-(0.530\,\frac{N}{m} )\cdot x}{7.90\,kg}

Velocity can be derived from the following definition of acceleration:

a = v\cdot \frac{dv}{dx}

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\frac{1}{2}\cdot v^{2} = \int\limits^{17\,m}_{0\,m} {\frac{18\,N-(0.530\,\frac{N}{m} )\cdot x}{7.90\,kg} } \, dx

\frac{1}{2}\cdot v^{2} =\frac{18\,N}{7.90\,kg}  \int\limits^{17\,m}_{0\,m}\, dx  - \frac{0.530\,\frac{N}{m} }{7.90\,kg} \int\limits^{17\,m}_{0\,m} {x} \, dx

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v =\sqrt{2\cdot[(2.278\,\frac{m}{s^{2}})\cdot x |_{0\,m}^{27\,m}-(0.034\,\frac{1}{s^{2}})\cdot x^{2}|_{0\,m}^{27\,m}]  }

The speed after the box has travelled 17 meters is:

v\approx 8.570\,\frac{m}{s}

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