Question

a large box whose mass is 20.0 kg rests on the frictionless floor. A mover pushes on the box with a force of 250 N at an angle 35.0 below the horizontal. Draw the box's free body diagram and calculate the acceleration of the box

b) if the kinetic friction coefficient is 0.1 between the box and floor. Draw the box's free body diagram and re-calculate the acceleration of the box

Answer #1

**Part (a)**

Gravitational acceleration = g = 9.81 m/s^{2}

Mass of the box = M = 20 kg

Force applied on the box = F = 250 N

Angle at which the force is applied = =
35^{o}

Acceleration of the box = a_{1}

From the free body diagram,

Ma_{1} = FCos

(20)a_{1} = 250Cos(35)

a_{1} = 10.24 m/s^{2}

**Part (b)**

Gravitational acceleration = g = 9.81 m/s^{2}

Mass of the box = M = 20 kg

Force applied on the box = F = 250 N

Angle at which the force is applied = =
35^{o}

Kinetic friction coefficient = = 0.1

Normal force on the box from the ground = N_{2}

Friction force on the box = f

f = N_{2}

Acceleration of the box = a_{2}

From the free body diagram,

N_{2} = Mg + FSin

f = N_{2}

f = (Mg + FSin)

Ma_{2} = FCos - f

Ma_{2} = FCos - (Mg +
FSin)

(20)a_{2} = 250Cos(35) - (0.1)[(20)(9.81) +
250Sin(35)]

a_{2} = 8.54 m/s^{2}

a) Acceleration of the box with no friction = 10.24
m/s^{2}

b) Acceleration of the box with friction present = 8.54
m/s^{2}

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