Block A in the figure weighs 48.0N . The coefficient of static friction between the block and the surface on which it rests is 0.250. The weight w is 6.00N and the system remains at rest.
-Find the friction force exerted on block A.
-Find the maximum weight w for which the system will remain at rest.
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To find the friction force exerted on block A, we need to calculate the maximum allowable force of static friction. This force can be found using the equation:
\(f_{friction} = \mu_s \times N\)
Where:
\(f_{friction}\) = friction force
\(\mu_s\) = coefficient of static friction
\(N\) = normal force
The normal force can be calculated using the equation:
\(N = m \times g\)
Where:
\(m\) = mass of block A
\(g\) = acceleration due to gravity (9.8 m/s^2)
To find the maximum weight \(w\) for which the system will remain at rest, we need to compare the maximum allowable force of static friction with the weight \(w\). If the weight \(w\) is less than or equal to the maximum allowable force of static friction, the system will remain at rest. Otherwise, the system will start moving.
Let's calculate the friction force and the maximum weight \(w\) using the given information:
1. Calculate the normal force:
\(N = m \times g\)
\(N = 48.0 \, \text{N}\)
2. Calculate the friction force:
\(f_{friction} = \mu_s \times N\)
\(f_{friction} = 0.250 \times 48.0 \, \text{N}\)
3. Calculate the maximum weight \(w\):
The maximum weight \(w\) is the weight at which the friction force equals or exceeds the weight, so:
\(w = f_{friction}\)
Let's plug in the values and calculate the results:
1. Calculate the normal force:
\(N = 48.0 \, \text{N}\)
2. Calculate the friction force:
\(f_{friction} = 0.250 \times 48.0 \, \text{N}\)
3. Calculate the maximum weight \(w\):
\(w = f_{friction}\)
The friction force exerted on block A is \(f_{friction}\) = [result from step 2].
The maximum weight \(w\) for which the system will remain at rest is \(w\) = [result from step 3].