A wooden block of mass 29.0 kg sits on a horizontal table. A wire of negligible mass is attached to the right side of the block and goes over a pulley (also of negligible mass, and frictionless), where it is allowed to dangle vertically. When a mass of 15.5 kg is attached to the dangling wire, the block on the table just barely starts to slide. What is the coefficient of static friction between the block and the table?
M1*g = M2*g*Us
Us = M1/M2 is the static friction coefficient
To find the coefficient of static friction between the block and the table, we need to analyze the forces acting on the block.
Let's start by determining the weight of the block. The weight (W) is given by the formula:
W = mass × gravitational acceleration
W = 29.0 kg × 9.8 m/s² (gravitational acceleration)
W = 284.2 N
Since the block is not moving initially, the static friction between the block and the table balances the component of the weight acting down the incline.
Next, when the mass of 15.5 kg is attached to the wire, it exerts a force on the block. This force is given by:
Force (F) = mass × gravity
F = 15.5 kg × 9.8 m/s² (gravitational acceleration)
F = 151.9 N
This force tries to pull the block to the right.
According to the problem, the block just barely starts to slide when this force is applied. That means the force of static friction (Fs) is at its maximum. When the block starts to slide, Fs will transition to kinetic friction.
The maximum force of static friction (Fs) can be expressed as:
Fs = coefficient of static friction × normal force
Since the block is on a horizontal table, the normal force (N) is equal to the weight of the block (W).
So, we can write:
Fs = coefficient of static friction × weight of the block
Now, equating the force of static friction with the force acting on the block, we have:
Fs = F
coefficient of static friction × W = F
coefficient of static friction × 284.2 N = 151.9 N
Solving for the coefficient of static friction (μs):
coefficient of static friction = F / W
coefficient of static friction = 151.9 N / 284.2 N
coefficient of static friction = 0.534
Therefore, the coefficient of static friction between the block and the table is approximately 0.534.