A 2.5 kg block is pulled to the right by a horizontal string. The coefficient of static friction between the block and the floor is 0.30 and the coefficient of kinetic friction is 0.20.
What value of force applied by the string will start the block moving?
To find the value of the force applied by the string that will start the block moving, we need to consider the forces acting on the block. The force applied by the string will oppose the force of static friction between the block and the floor until it reaches its maximum value and overcomes it, causing the block to start moving.
The maximum force of static friction can be calculated using the formula:
\(F_{\text{friction}} = \mu_s \cdot F_{\text{normal}}\),
where \(\mu_s\) is the coefficient of static friction and \(F_{\text{normal}}\) is the normal force acting on the block.
The normal force in this case is equal to the weight of the block, which can be calculated using the formula:
\(F_{\text{normal}} = m \cdot g\),
where \(m\) is the mass of the block and \(g\) is the acceleration due to gravity (approximately \(9.8 \, \text{m/s}^2\)).
Substituting the given values:
\(m = 2.5 \, \text{kg}\),
\(\mu_s = 0.30\),
\(g \approx 9.8 \, \text{m/s}^2\),
we can calculate the maximum force of static friction:
\(F_{\text{friction}} = 0.30 \cdot (2.5 \, \text{kg} \cdot 9.8 \, \text{m/s}^2)\).
Now, since we are looking for the force applied by the string that will start the block moving, we need to apply a force greater than the maximum force of static friction. In this case, we can choose any value greater than the maximum force of static friction. Let's say we choose a force of \(F_{\text{applied}} = 20 \, \text{N}\).
Therefore, a force of \(F_{\text{applied}} = 20 \, \text{N}\) applied by the string will start the block moving.