The coefficient of static friction can be determined using the following procedure. A block is held against a vertical wall by compressing a spring attached to the block.
If the spring has a spring constant = 531 N/m and requires a compression of 3.7 cm to just keep the block from slipping, what is the static friction coefficient between the wall and the 4.5 kg block?
To determine the static friction coefficient between the wall and the block, we can use the following steps:
Step 1: Find the force exerted by the spring.
The force exerted by the spring can be calculated using Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement from equilibrium and the spring constant.
Given:
- Spring constant (k) = 531 N/m
- Compression of the spring (x) = 3.7 cm = 0.037 m
Using Hooke's Law:
Force (F) = k * x
Substituting the given values:
F = 531 N/m * 0.037 m
F = 19.647 N (rounded to three decimal places)
Step 2: Find the magnitude of the force of gravity.
The force of gravity can be calculated using the formula:
Force of gravity (mg) = mass (m) * acceleration due to gravity (g)
Given:
- Mass (m) = 4.5 kg
- Acceleration due to gravity (g) = 9.8 m/s^2
Calculating the force of gravity:
mg = 4.5 kg * 9.8 m/s^2
mg = 44.1 N
Step 3: Determine the magnitude of the static friction force.
When a block is just about to slip, the static friction force is equal in magnitude but opposite in direction to the applied force. Since the applied force is provided by the compressed spring, we can say that the magnitude of the static friction force is equal to the force exerted by the spring.
Frictional force (f) = 19.647 N
Step 4: Calculate the coefficient of static friction.
The coefficient of static friction (μs) between two surfaces can be calculated using the formula:
Coefficient of static friction (μs) = static friction force / normal force
In this case, the normal force is equal to the force of gravity acting on the block.
Using the values we calculated earlier:
μs = 19.647 N / 44.1 N
μs = 0.445 (rounded to three decimal places)
Therefore, the static friction coefficient between the wall and the 4.5 kg block is approximately 0.445.
To determine the static friction coefficient between the wall and the block, you need to follow these steps:
Step 1: Calculate the force exerted by the spring:
Using Hooke's Law, we know that the force exerted by a spring can be calculated using the formula:
F = k * x
where F is the force, k is the spring constant, and x is the compression of the spring.
In this case, the spring constant (k) is given as 531 N/m and the compression (x) is 3.7 cm. However, we need to convert the compression to meters to match the units of the spring constant:
x = 3.7 cm * (1 m / 100 cm) = 0.037 m
Now, we can calculate the force exerted by the spring:
F = 531 N/m * 0.037 m = 19.647 N
Step 2: Calculate the weight of the block:
The weight of the block can be calculated using the formula:
weight = mass * acceleration due to gravity
Given that the mass of the block is 4.5 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight:
weight = 4.5 kg * 9.8 m/s^2 = 44.1 N
Step 3: Determine the static friction force:
Since the block is just on the verge of slipping, the static friction force is equal to the force exerted by the spring (F). Therefore, the static friction force is 19.647 N.
Step 4: Calculate the static friction coefficient:
The static friction coefficient (μs) can be calculated using the formula:
μs = static friction force / normal force
In this case, the normal force is equal to the weight of the block (44.1 N).
μs = 19.647 N / 44.1 N ≈ 0.445
Therefore, the static friction coefficient between the wall and the 4.5 kg block is approximately 0.445.
at the slip point , friction force = gravitational force
let μ = static friction coefficient
531 N/m * .037 m = 4.5 kg * g * μ