an electric motor is used to pull a 125 kg box across a floor using a long cable. the tension in the cable is 350 N amd the box accelerates at 1.2 m/s^2 [forward] for 5 seconds. the cable breaks and the box slows down and stops. calculate the coefficient of kinetic friction?

Wb = mg = 125kg * 9.8N/kg = 1225N. =

Weight of box.

Fb = (1225N,0deg.).
Fp = Fh = 1225sin(0) = 0 = Force parallel to plane = hor. force.
Fv = 1225cos(0) = 1225N = Force perpendicular to plane = The normal.

Fn = ma = 125 * 1.2 = 150N = Net force.
Fn = Fap - Fp - Ff = 150N,
350 - 0 - Ff = 150,
Ff = 350 - 150 = 200N,
Ff = u*Fv = 200,
1225*u = 200,
u = 0.163 = Coefficient of friction.

Fap = Force applied.

To calculate the coefficient of kinetic friction, we need to use the equations of motion and consider the forces acting on the box. Let's break down the problem step by step:

Step 1: Find the net force acting on the box.
The net force acting on the box can be determined using Newton's second law of motion: F_net = m * a, where F_net is the net force, m is the mass of the box, and a is the acceleration of the box.

Given:
Mass of the box (m) = 125 kg
Acceleration of the box (a) = 1.2 m/s^2

Using the formula, we can calculate the net force:
F_net = m * a
F_net = 125 kg * 1.2 m/s^2
F_net = 150 N

Step 2: Determine the force of friction.
The tension in the cable (T) provides the force that is opposing the forward motion of the box. When the cable broke, there is no force pulling the box anymore, so the only force acting on the box is the force of kinetic friction (F_friction).

Given:
Tension in the cable (T) = 350 N

Since the net force is equal to the force of friction acting in the opposite direction:
F_friction = F_net
F_friction = 150 N

Step 3: Calculate the coefficient of kinetic friction.
The force of friction can be calculated using the equation F_friction = μ_k * N, where μ_k is the coefficient of kinetic friction and N is the normal force acting on the box.

However, we need to calculate the normal force first. In this case, since the box is on a flat floor and there is no vertical motion, the normal force is equal in magnitude and opposite in direction to the weight of the box.

The weight of the box (F_weight) can be calculated using the equation F_weight = m * g, where m is the mass of the box and g is the acceleration due to gravity (around 9.8 m/s^2).
F_weight = 125 kg * 9.8 m/s^2
F_weight = 1225 N

Since the normal force is equal in magnitude and opposite in direction to the weight of the box, the normal force (N) is 1225 N as well.

Now we can solve for the coefficient of kinetic friction:
F_friction = μ_k * N
150 N = μ_k * 1225 N

Dividing both sides by 1225 N:
μ_k = 150 N / 1225 N
μ_k = 0.122

Therefore, the coefficient of kinetic friction is approximately 0.122.

To calculate the coefficient of kinetic friction, we can use the following equation:

μk = Fk / (m * g)

Where:
μk is the coefficient of kinetic friction,
Fk is the force of kinetic friction,
m is the mass of the box, and
g is the acceleration due to gravity.

Given:
Mass of the box (m) = 125 kg
Force of tension (T) = 350 N
Acceleration (a) = 1.2 m/s^2 (forward)
Time (t) = 5 seconds

Step 1: Calculate the net force on the box.
Using Newton's second law of motion:
Fnet = m * a
Fnet = (125 kg) * (1.2 m/s^2)
Fnet = 150 N

Step 2: Calculate the force of kinetic friction.
Using the equation:
Fnet = Fk - T
150 N = Fk - 350 N
Fk = 150 N + 350 N
Fk = 500 N

Step 3: Calculate the coefficient of kinetic friction.
μk = Fk / (m * g)
μk = 500 N / (125 kg * 9.8 m/s^2)
μk = 0.408

Therefore, the coefficient of kinetic friction is approximately 0.408.