A 13.9 kg block is dragged over a rough, horizontal surface by a 70.7 N force acting at 19.8 degrees above the horizontal. The block is displaced 4.55 m, and the coefficient of kinetic friction is 0.298.

How much energy is lost due to friction?

break the 70.7N force into vertical and horizontal components.

The vertical component reduces weight, so figure the normal force (and friction) from that.

frictionforce=(13.9g-70.7Sin19.8)mu
work=frictionforce*distance

Now notice that this does not equal the horizontal component of force*distance. So, the block has to accelerate.

To find how much energy is lost due to friction, we need to calculate the work done by the friction force.

The work done by a force (W) is equal to the force (F) multiplied by the displacement (d) and the cosine of the angle (θ) between the force and the displacement:

W = F * d * cos(θ)

In this case, the friction force (Ff) can be calculated using the equation:

Ff = coefficient of kinetic friction * normal force

The normal force (Fn) is equal to the weight of the block (mg), where m is the mass of the block and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Now, let's calculate the normal force:

Fn = m * g
Fn = 13.9 kg * 9.8 m/s^2
Fn ≈ 136.22 N

Next, we can calculate the friction force:

Ff = coefficient of kinetic friction * Fn
Ff = 0.298 * 136.22 N
Ff ≈ 40.57 N

The angle between the force and displacement is 19.8 degrees, so we need to convert to radians:

θ = 19.8 degrees * (π/180 degrees)
θ ≈ 0.345 rad

Finally, we can calculate the work done by the friction force:

W = Ff * d * cos(θ)
W = 40.57 N * 4.55 m * cos(0.345 rad)
W ≈ 162.97 J

Therefore, the amount of energy lost due to friction is approximately 162.97 Joules.