A 4.0kg block of wood sits on a table A string is tied to the wood, running over a pulley and down to a hanging object. The greatest mass that can be hung from the string without moving the block of wood is 1.8 kg. Calculate the coeffcient of static friction between the block of wood and the table.
To solve this problem, we will set up an equation using the forces acting on the block of wood.
First, let's consider the forces acting on the block of wood. We have the force of gravity (mg) pulling the block downward, the normal force (N) exerted by the table pushing the block upward, and the static friction force (f_s) opposing the force of gravity.
Since the block is not moving, the force of static friction must be equal to the force of gravity:
f_s = mg
Where:
m = mass of the block of wood = 4.0 kg
g = acceleration due to gravity = 9.8 m/s^2
f_s = 4.0 kg * 9.8 m/s^2
f_s = 39.2 N
Now, let's consider the forces acting on the hanging object. We have the tension in the string (T) pulling the hanging object upward and the force of gravity (m_object * g) pulling the object downward.
The maximum mass that can be hung from the string without moving the block of wood is when the force of static friction is at its maximum. Therefore, the tension in the string (T) must be equal to the force of static friction (f_s):
T = f_s
From the problem, we know that the maximum mass that can be hung from the string without moving the block of wood is 1.8 kg. Therefore, the weight of the hanging object (m_object * g) must be equal to the tension in the string (T):
m_object * g = T
Where:
m_object = maximum mass that can be hung from the string without moving the block of wood = 1.8 kg
Setting up the equation:
1.8 kg * 9.8 m/s^2 = f_s
Solving for f_s:
f_s = 17.64 N
Now, we can solve for the coefficient of static friction (μ_s) using the equation:
f_s = μ_s * N
Rearranging the equation:
μ_s = f_s / N
Where
N = Normal force exerted by the table
Since the block of wood is not moving vertically, the normal force (N) is equal to the force of gravity acting on the block:
N = mg
Substituting the values:
μ_s = 39.2 N / (4.0 kg * 9.8 m/s^2)
Solving for μ_s:
μ_s ≈ 1.0
Therefore, the coefficient of static friction between the block of wood and the table is approximately 1.0.