A cable attached to a block of mass 16.35 kg pulls the block along a horizontal floor at a constant velocity. If the tension in the cable is 9.36 N, what is the coefficient of kinetic friction between the block and the floor?
not sure how to do this one
... I am thinking I use Sum of all Forces = T = ma =F(friction)= -ìkN
Wb = mg = 16.36kg * 9.8N/kg = 160.2N =
Wt. of block.
Fp = 160sin(0) = 0 Newtons. = Force
parallel to plane.
Fv = 160cos(0) = 160N. = Force perpen-
dicular to plane.
Fn = Fap - Fp - Ff = ma = 0(a = 0).
9.36 - 0 - Ff = 0,
Ff = uFv = 9.36,
u*160 = 9.36,
u = 0.0585 = Force of friction.
Fn = Net force.
Fap = Force applied.
To find the coefficient of kinetic friction between the block and the floor, you need to use the equation for the sum of forces acting on the block along the horizontal direction.
First, let's identify the forces acting on the block. There are two forces involved: the tension in the cable (T) and the force of kinetic friction (F_friction).
Given information:
- Mass of the block (m) = 16.35 kg
- Tension in the cable (T) = 9.36 N
The sum of forces equation is:
Sum of forces = T - F_friction = ma
Since the block is moving at a constant velocity, we know that the acceleration (a) is zero. Therefore, the sum of forces equation simplifies to:
T - F_friction = 0
Now, we can solve for the force of kinetic friction (F_friction) by rearranging the equation:
F_friction = T
Substituting the given values:
F_friction = 9.36 N
The force of kinetic friction can also be written as:
F_friction = μ_k * N
Where μ_k is the coefficient of kinetic friction and N is the normal force exerted by the floor on the block. Since the block is on a horizontal floor, the normal force is equal to the weight of the block, which is given by:
N = mg
Substituting the given values:
N = 16.35 kg * 9.8 m/s^2
N = 160.23 N
Now, we can determine the coefficient of kinetic friction by rearranging the equation:
μ_k = F_friction / N
Substituting the known values:
μ_k = 9.36 N / 160.23 N
Calculating this division:
μ_k ≈ 0.058
Therefore, the coefficient of kinetic friction between the block and the floor is approximately 0.058.