if the weight of the block,W,is 2.5 kilogram,the coefficient of static friction,0.25,and the coefficient of kinetic friction,0.15,determine: (a) the force necessary to hold the block sliding down (b) the force necessary to pull the block up the plane with uniform speed
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To determine the force necessary to hold the block sliding down the plane, we need to consider the force of gravity and the force of static friction.
(a) Force to hold the block sliding down:
Step 1: Calculate the force of gravity acting on the block.
The force of gravity is given by the formula: F_gravity = mass x acceleration due to gravity.
In this case, the mass (m) of the block is given as 2.5 kg, and the acceleration due to gravity (g) is approximately 9.8 m/s^2.
Therefore, F_gravity = 2.5 kg x 9.8 m/s^2 = 24.5 N.
Step 2: Calculate the maximum force of static friction.
The maximum force of static friction (F_static) can be found using the coefficient of static friction (μ_static) and the normal force (F_normal).
The normal force is given by the formula: F_normal = mass x acceleration due to gravity.
Therefore, F_normal = 2.5 kg x 9.8 m/s^2 = 24.5 N.
The maximum force of static friction can be calculated as: F_static = μ_static x F_normal.
Given that the coefficient of static friction (μ_static) is 0.25, substituting the values we have: F_static = 0.25 x 24.5 N = 6.125 N.
Therefore, the force necessary to hold the block sliding down is 6.125 N.
(b) Force necessary to pull the block up the plane with uniform speed:
To determine the force necessary to pull the block up the plane with uniform speed, we need to consider the force of gravity and the force of kinetic friction.
Step 1: Calculate the force of gravity acting on the block.
As before, the force of gravity is given by the formula: F_gravity = mass x acceleration due to gravity.
In this case, the mass (m) of the block is still 2.5 kg, and the acceleration due to gravity (g) is approximately 9.8 m/s^2.
Therefore, F_gravity = 2.5 kg x 9.8 m/s^2 = 24.5 N.
Step 2: Calculate the force of kinetic friction.
The force of kinetic friction (F_kinetic) can be found using the coefficient of kinetic friction (μ_kinetic) and the normal force (F_normal) as well.
In this case, the coefficient of kinetic friction (μ_kinetic) is given as 0.15, and the normal force (F_normal) remains the same as calculated before, which is 24.5 N.
So, F_kinetic = μ_kinetic x F_normal = 0.15 x 24.5 N = 3.675 N.
Therefore, the force necessary to pull the block up the plane with uniform speed is 3.675 N.