A block of 1kg is kept on another block of 2kg in a horizontal surface. Coefficient of friction between two blocks is 0.4. The blocks are given velocities of 2m/s and 8m/s in same direction.The time when relative motion between them will stop =..???
which at 2 and which at 8?
assuming the small one is at 2
and the big one at 8
normal force = 9.81 N
friction force = .4*9.81 = 3.92 N
forward force on top small block = 3.92
a of small block = 3.92/1 = 3.92 m/s^2
so speed of small block = 2 + 3.92 t
back force on big block = -3.92 N
a of big block = - 3.92/2 = -1.96 m/s^2
so speed of big blok = 8 - 1.96 t
so we want to know t when
2 + 3.92 t = 8 - 1.96 t
To find the time when the relative motion between the two blocks will stop, we need to analyze the forces acting on the system.
First, let's consider the force of friction between the two blocks. The force of friction can be calculated using the equation:
force of friction = coefficient of friction * normal force
The normal force acting on the top block can be calculated using the equation:
normal force = mass * gravity
where gravity is the acceleration due to gravity (9.8 m/s^2).
In this case, the normal force on the top block is equal to the weight of the top block, which can be calculated using the formula:
weight = mass * gravity
Now, let's calculate the force of friction between the blocks:
force of friction = coefficient of friction * normal force
Next, let's analyze the forces acting on the blocks. The force acting on the top block is the force of friction, which opposes the motion. The force acting on the bottom block is the force exerted by the top block, which is equal to the mass of the top block multiplied by its acceleration.
We can use Newton's second law to relate the force, mass, and acceleration:
force = mass * acceleration
Setting the force of friction equal to the force exerted by the top block, we can solve for the acceleration:
force of friction = mass * acceleration
Now, we have two important equations:
force of friction = coefficient of friction * normal force
force of friction = mass * acceleration
Substituting the expressions for the normal force and the weight, we can solve for the acceleration:
coefficient of friction * mass * gravity = mass * acceleration
Simplifying the equation, we find:
coefficient of friction * gravity = acceleration
Now, we know the acceleration of the system. Since the blocks were given velocities in the same direction, they will eventually come to a stop when the velocity of the top block becomes equal to the velocity of the bottom block. We can calculate the time it takes for this to happen using the equation:
time = (final velocity - initial velocity) / acceleration
In this case, the initial velocity of the top block is 2 m/s, and the final velocity is 8 m/s (since the velocities are in the same direction). The acceleration is given by the equation above.
Plugging in the values, we can calculate the time it takes for the relative motion between the blocks to stop.