A 136kg crate is at rest on a floor.A man attempts to push it across the floor by applying 412N force horizontally. Taking the coefficient of static friction between the crate and the floor to be 0.37,show that the crate does not move.
pushing force=412
max static frictioni=136*9.8*.37= ...... N
if the pushing force is not greater than the max static friction, it wont move.
M*g = 136*9.8 = 1333 N. = Wt. of crate = Normal force(Fn).
Fs = u*Fn = 0.37 * 1333 = 493 N. = Force of static friction.
F - Fs > M*a.
F - 493 >M*0,
F > 493 N.
So, the min. pushing force (F) must be greater than the force of static friction(Fs).
To determine whether the crate will move or not, we need to compare the applied force to the maximum static friction force. If the applied force is greater than the maximum static friction force, the crate will start moving. However, if the applied force is equal to or less than the maximum static friction force, the crate will not move.
The maximum static friction force between the crate and the floor can be calculated using the formula:
Maximum static friction force (Fsmax) = coefficient of static friction (μ) × normal force (N)
In this case, the normal force is equal to the weight of the crate, given by:
Weight (W) = mass (m) × acceleration due to gravity (g)
Given that the mass of the crate is 136 kg and the acceleration due to gravity is approximately 9.8 m/s², we can calculate the weight as follows:
W = 136 kg × 9.8 m/s² = 1332.8 N
Now, we can calculate the maximum static friction force:
Fsmax = μ × N = 0.37 × 1332.8 N ≈ 492.9 N
The applied force is given as 412 N, which is less than the maximum static friction force (492.9 N). Therefore, the crate does not move because the applied force is not enough to overcome the maximum static friction force.