a force of 5 N is required to slide a block at constant speed over the dry surface of a table. The block has a mass of 2.5 kg. The coefficient of friction is..
2.0
To find the coefficient of friction, we can use the formula:
\( f = \mu \times N \)
where
\( f \) = force of friction,
\( \mu \) = coefficient of friction, and
\( N \) = normal force.
In this case, the force of friction is equal to the applied force of 5 N. The normal force is the weight of the block, given by:
\( N = m \times g \)
where
\( m \) = mass of the block, and
\( g \) = acceleration due to gravity (approximated as 9.8 m/s²).
Plugging in the values:
\( N = 2.5 \, \text{kg} \times 9.8 \, \text{m/s²} = 24.5 \, \text{N} \)
Now, we can rearrange the formula to solve for the coefficient of friction:
\( \mu = \frac{f}{N} = \frac{5 \, \text{N}}{24.5 \, \text{N}} \approx 0.204 \) (rounded to three decimal places).
Therefore, the coefficient of friction between the block and the dry surface of the table is approximately 0.204.
To find the coefficient of friction, we can use the equation that relates the force of friction to the normal force and the coefficient of friction. The formula is:
Force of friction = coefficient of friction x normal force
In this case, the force required to slide the block at constant speed is given as 5 N. We know the mass of the block is 2.5 kg. To find the normal force acting on the block, we need to consider the gravitational force.
The formula for the force of gravity is:
Force of gravity = mass x acceleration due to gravity
where the acceleration due to gravity is approximately 9.8 m/s^2.
Now, we can calculate the force of gravity acting on the block:
Force of gravity = 2.5 kg x 9.8 m/s^2 = 24.5 N
Since the block is not accelerating vertically, the normal force and the force of gravity are equal in magnitude but opposite in direction. Therefore, the normal force is also 24.5 N.
Now we have all the necessary values to find the coefficient of friction:
Force of friction = coefficient of friction x normal force
5 N = coefficient of friction x 24.5 N
Now, divide both sides of the equation by 24.5 N:
coefficient of friction = 5 N / 24.5 N
coefficient of friction ≈ 0.204
Therefore, the coefficient of friction between the block and the dry surface of the table is approximately 0.204.