The coefficient of static friction between a block and a horizontal floor is 0.40, while the coefficient of kinetic friction is 0.15. The mass of the block is 5.0 kg. A horizontal force is applied to the block and slowly increased. (a) What is the value of the applied horizontal force at the instant that the block starts to slide? (b) What is the net force on the block after it starts to slide?
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To find the value of the applied horizontal force when the block starts to slide, we need to determine the maximum force of static friction first. The maximum force of static friction can be found using the formula:
Maximum force of static friction = coefficient of static friction × normal force
Since the block is on a horizontal floor, the normal force is equal to the weight of the block. The weight of the block can be found using the formula:
Weight = mass × gravitational acceleration
Therefore, the weight of the block is:
Weight = 5.0 kg × 9.8 m/s^2 = 49 N
Now, we can calculate the maximum force of static friction:
Maximum force of static friction = 0.40 × 49 N = 19.6 N
Therefore, the value of the applied horizontal force at the instant the block starts to slide is 19.6 Newtons (N).
After the block starts to slide, the force of friction changes from static to kinetic friction. The force of kinetic friction can be found using the formula:
Force of kinetic friction = coefficient of kinetic friction × normal force
Again, the normal force is equal to the weight of the block, which is 49 N. Therefore, the force of kinetic friction is:
Force of kinetic friction = 0.15 × 49 N = 7.35 N
Since the block is already in motion, the net force on the block is equal to the applied force minus the force of kinetic friction:
Net force = Applied force - Force of kinetic friction
Therefore, the net force on the block, after it starts to slide, is:
Net force = 19.6 N - 7.35 N = 12.25 N