A 40 kg slab rests on a friction less floor.a 10 kg block rests on top of the slab.the coefficient kinetic friction between the block and the slab is 0.40.a horizontal force of 100N is applied on the 10 kg block.find the resulting acceleration of the slab.

Remember shortcut.... In this kind of case... Acceleration=(coefficient of friction*m1*g)/m2.....

So. a=(.4*10*10)/40=1m/s²

Given m =10 kg

And we have F = Uķmg
=0.40×10 ×10
=40N
And, F= ma
a=F/m= 40/40= 1 m/s^2

mass of block = 10Kg

F = (coefficient of friction)* mg
=0.40*10*10
=40N
By F = ma
a = F/m = 40/40 = 1 m/s^2

To find the resulting acceleration of the slab, we will follow these steps:

Step 1: Calculate the net force acting on the 10 kg block.
Step 2: Calculate the friction force between the block and the slab.
Step 3: Calculate the net force acting on the slab.
Step 4: Calculate the resulting acceleration of the slab.

Let's begin:

Step 1: Calculate the net force acting on the 10 kg block.
The net force is given by the equation:
Net force = Applied force - Friction force

We are given that the applied force is 100N. To calculate the friction force, we need to multiply the coefficient of kinetic friction (0.40) by the normal force between the block and the slab.

Normal force = Weight of the block = mass of the block * acceleration due to gravity
= 10 kg * 9.8 m/s^2
= 98 N

Friction force = Coefficient of kinetic friction * Normal force
= 0.40 * 98 N
= 39.2 N

Net force = 100 N - 39.2 N
= 60.8 N

Step 2: Calculate the friction force between the block and the slab.
The friction force between the block and the slab is equal to the net force acting on the block, as there is no friction on the floor.

Friction force = Net force on the block = 60.8 N

Step 3: Calculate the net force acting on the slab.
The net force acting on the slab is equal to the friction force between the block and the slab.

Net force on the slab = Friction force = 60.8 N

Step 4: Calculate the resulting acceleration of the slab.
To find the acceleration, we can use Newton's second law, which states that the net force is equal to the mass of the object multiplied by its acceleration.

Net force on the slab = mass of the slab * acceleration of the slab

We are given the mass of the slab as 40 kg and the net force on the slab as 60.8 N.

60.8 N = 40 kg * acceleration of the slab

Simplifying the equation and solving for acceleration of the slab:

acceleration of the slab = 60.8 N / 40 kg
= 1.52 m/s^2

Therefore, the resulting acceleration of the slab is 1.52 m/s^2.

Bad worst

Normal reaction from 40 kg slab on 10 kg block = 10 * 9.81 = 98.1 N

Static frictional force = 98.1 * 0.6 N is less than 100 N applied
=> 10 kg blck will slide on 40 kg slab and net force on it
= 100 N - kinetic friction
= 100 - 98.1 * 0.4 = 61 N
=> 10 kg block will slide on 40 kg slab with 61/10 = 6.1 m/s

Frictional force on 40 kg slab by 10 kg block = 98.1 * 0.4 = 39 N
=> 40 kg slab will move with
39/40 m/s²
= 0.98 m/s²

m*g = 10kg * 9.8N/kg = 98 N. = Wt. of the block.

Fk = u*mg = 0.40 * 98 = 39.2 N. = Force
of kinetic friction.

a = Fk/Ms = 39.2/40 = 0.98 m/s^2.