A string is tied to a 4.4 kg block and a 120 g bucket from a pulley. Students add 20 g washers one at a time to the bucket. the students are unaware that the coefficient of static friction for the block on the table is 0.42.
a) what is the maximum force of static friction for the block?
b) how many washers can the students add to the bucket without moving the block.
To find the maximum force of static friction for the block, we need to calculate the maximum force that can be applied before the block starts moving.
a) To calculate the maximum force of static friction, we use the equation:
F_friction = μ * F_normal,
where F_friction is the force of friction, μ is the coefficient of static friction, and F_normal is the normal force.
The normal force is the force exerted by the table on the block, which is equal to the weight of the block (mg), where m is the mass of the block and g is the acceleration due to gravity.
F_normal = m * g,
where m is the mass of the block (4.4 kg) and g is the acceleration due to gravity (9.8 m/s^2).
F_normal = 4.4 kg * 9.8 m/s^2 = 43.12 N.
Now we can calculate the maximum force of static friction:
F_friction = μ * F_normal.
F_friction = 0.42 * 43.12 N = 18.10 N.
Therefore, the maximum force of static friction for the block is 18.10 N.
b) To find how many washers can be added to the bucket without moving the block, we need to consider the force balance.
The force balance is given by:
F_applied + F_friction = F_tension,
where F_applied is the force applied by the students (the weight of the washer), F_friction is the force of friction, and F_tension is the tension in the string.
Since we want to find the maximum number of washers that can be added without moving the block, we need to find the maximum force applied (F_applied) that still maintains the block at rest.
F_applied is equal to the force of gravity acting on the bucket (mass of the bucket * gravitational acceleration).
F_applied = m_bucket * g,
where m_bucket is the mass of the bucket (0.120 kg) and g is the acceleration due to gravity (9.8 m/s^2).
F_applied = 0.120 kg * 9.8 m/s^2 = 1.176 N.
Now, we can calculate the tension in the string (F_tension) when the block is at rest:
F_tension = F_applied + F_friction.
F_tension = 1.176 N + 18.10 N = 19.276 N.
Since each washer adds an additional force of 0.02 kg * 9.8 m/s^2 = 0.196 N, we can find the maximum number of washers by dividing the maximum tension by the force added by each washer:
Max Number of Washers = (F_tension - F_applied) / force added per washer.
Max Number of Washers = (19.276 N - 1.176 N) / 0.196 N = 94.
Therefore, the students can add a maximum of 94 washers to the bucket without moving the block.