Fa E Book

Help with physics question. See if I did right. Keep getting wrong answer.?

A student pulls a box of books with a force of 120N [E]. The box of has a mass of 20kg. The coefficient of kinetic friction between the box and floor is 0.5. a) Find the acceleration of box.
b) What if he pulls with a force of 120N [E30N].
a)
Fg = Force Gravity
Fn = Force normal
a = acceleration
Fnet = Net force
Ff = Frictional force
u = Coefficient

The first step with a problem like this is to draw a free body diagram, but since I don’t know how to draw in the given format I will describe the diagram to the best of my ability.

Consider the box of books to be a point mass at the origin. The student pulls with a force of 120N in the positive x direction (right). Since the box is on a surface, the Normal force (N) will be equal and opposite the Force due to gravity (Weight, W) The frictional force (f) acts against the force in the positive x direction, so this force goes left.

This can be shown mathematically by equations of sums of forces in particular directions.

∑Fy = N – W = 0 This equation says that the y direction is in static equilibrium meaning that the acceleration is 0. This equation confirms that the Normal force is equal to the weight. W = mg

thus…

N = mg

The frictional force is equal to the normal force times the coefficient of friction f = Nu = mgu

∑Fx = F – f = ma There is motion in this direction thus the sum of the forces equals the mass times the acceleration according to Newton’s 2nd law

F – mgu = ma

120 – (20kg)(9.81m/s/s)(.5) = (20kg)a
1.095 m/s/s = a

For part b the applied force is now at an angle and we need to incorporate the vector components of the force…there is still no motion in the y direction but the normal force will change slightly

∑Fy = N + Fsin30 – W = 0

N = W – Fsin30 = mg – 120sin30 = 20kg(9.81m/s/s) – 120(1/2) = 136.2

f = Nu = 136.2(.5) = 68.1N

The sum of the forces in the x direction will change slightly as well

∑Fx = Fcos30 – f = ma

103.923 – 68.1 = (20kg)a

35.82305N / 20kg = a

a = 1.79 m/s/s

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