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dsp73
3 years ago
6

A student pulls on a rope attached to a box of books and moves the box down the hall. The student pulls with a force of 185N at

an angle of 25 above the horizontal. The box has a mass of 35.0kg and a the coefficient of kinetic frictino between the box and the floor is 0.27. Find the acceleration of the box
Physics
1 answer:
Vitek1552 [10]3 years ago
8 0

Answer:

2.75 m/s^2

Explanation:

We can solve the problem by writing the equations of motion along the horizontal and vertical direction.

Along the horizontal direction we have:

T cos \theta - \mu N = ma (1)

where

T cos \theta is the horizontal component of the tension, where

T = 185 N is the tension in the rope

\theta=25^{\circ} is the angle between the rope and the horizontal

\mu N is the force of friction, where

\mu=0.27 is the coefficient of friction

N is the normal reaction of the floor on the box

m = 35.0 kg is the mass of the box

a is the acceleration

Along the vertical direction we have:

N+T sin \theta-mg=0 (2)

where

N is the normal force (upward direction)

T sin \theta is the vertical  component of the tension in the rope (upward direction)

mg is the weight of the box (downward direction), where

m = 35.0 kg is the mass of the box

g=9.8 m/s^2 is the acceleration due to gravity

From eq.(2) we get:

N=mg-T sin \theta

And substituting into (1), we can find the acceleration:

T cos \theta - \mu (mg-T sin \theta) = ma\\Tcos \theta -\mu mg + \mu T sin \theta = ma\\a=\frac{T cos \theta- \mu mg + \mu T sin \theta}{m}=\\=\frac{(185)(cos 25^{\circ})-(0.27)(35.0)(9.8)+(0.27)(185)(sin 25^{\circ})}{35.0}=2.75 m/s^2

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