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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The answer to a part is 2 newton
The answer to a part is 20 newton
To answer these questions, we'll need to use the equations of static and kinetic friction, as well as the concept of net force. Let's break it down step by step:
(a) What is the value of the applied horizontal force at the instant that the block starts to slide?
When the block is at rest or on the verge of sliding, the force of static friction counteracts the applied force until it reaches its maximum value. This maximum value is given by:
Fs_max = μs * N,
Where μs is the coefficient of static friction, and N is the normal force exerted on the block by the surface (in this case, the floor).
The normal force, N, is equal to the weight of the object, which is the mass (m) multiplied by the acceleration due to gravity (g):
N = m * g,
Substituting the given values:
N = 5.0 kg * 9.8 m/s^2 = 49 N.
Then, we can calculate the maximum force of static friction:
Fs_max = 0.40 * 49 N = 19.6 N.
Therefore, the value of the applied horizontal force at the instant that the block starts to slide is 19.6 N.
(b) What is the net force on the block after it starts to slide?
Once the block starts to slide, the force of static friction is replaced by the force of kinetic friction, which is given by:
Fk = μk * N,
Where μk is the coefficient of kinetic friction, and N is the normal force.
Using the same values as before, we can calculate the force of kinetic friction:
Fk = 0.15 * 49 N = 7.35 N.
The net force on the block after it starts to slide is the force applied minus the force of kinetic friction:
Net force = Applied force - Force of kinetic friction,
Net force = 19.6 N - 7.35 N = 12.25 N.
Therefore, the net force on the block after it starts to slide is 12.25 N.