A 7.40-kg block is placed on top of a 12.5-kg block that rests on a frictionless table. The coefficient of static friction between the two blocks is 0.610. What is the maximum horizontal force that can be applied before the 7.40-kg block begins to slip relative to the 12.5-kg block, if the force is applied to (a) the more massive block and(b) the less massive block?
force friction between two blocks:
7.40*9.8*.610=44.3N
maximum acceleration: 44.3=7.40*a or
a= 5.99m/s^2
a) force=ma
force=(7.4+12.5)5.99
b) force= 7.4*5.99
To find the maximum horizontal force applied before the 7.40-kg block begins to slip relative to the 12.5-kg block, we need to consider the force of friction.
The force of friction between the two blocks can be found using the equation: Frictional force = coefficient of static friction * normal force.
The normal force is equal to the weight of the block above it, so the normal force on the 7.40-kg block is equal to its weight (mass * gravity), and the normal force on the 12.5-kg block is equal to the sum of its weight and the weight of the block above it.
(a) If the force is applied to the more massive block (12.5-kg block):
The maximum force that can be applied to the more massive block before the 7.40-kg block begins to slip is equal to the force of friction between the two blocks.
Frictional force between the blocks = coefficient of static friction * normal force on the 12.5-kg block.
Normal force on the 12.5-kg block = weight of 12.5-kg block + weight of 7.40-kg block.
Weight of 12.5-kg block = mass of 12.5-kg block * gravity.
Weight of 7.40-kg block = mass of 7.40-kg block * gravity.
Substitute the values and calculate the normal force:
Normal force on the 12.5-kg block = (12.5 kg * 9.8 m/s²) + (7.40 kg * 9.8 m/s²).
Next, calculate the maximum force:
Maximum force = coefficient of static friction * normal force on the 12.5-kg block.
Substitute the values and calculate the maximum force.
(b) If the force is applied to the less massive block (7.40-kg block):
The maximum force that can be applied to the less massive block before the 7.40-kg block begins to slip is equal to the force of friction between the two blocks.
Frictional force between the blocks = coefficient of static friction * normal force on the 7.40-kg block.
Normal force on the 7.40-kg block = weight of 7.40-kg block.
Calculate the maximum force:
Maximum force = coefficient of static friction * normal force on the 7.40-kg block.
Substitute the values and calculate the maximum force.
By following these steps, you can find the maximum horizontal force that can be applied before the blocks begin to slip relative to each other, whether the force is applied to the more massive or less massive block.