Two blocks with masses m1 = 1.40 kg and m2 = 3.00 kg are connected by a massless string, as shown in the Figure. They are released from rest. The coefficent of kinetic friction between the upper block and the surface is 0.390.In the figure m1 is on top of a horizontal table with a pully connecting m1 and m2 which is hanging off the edge of the table.
Assume that the pulley has a negligible mass and is frictionless, and calculate the speed of the blocks after they have moved a distance 20.0 cm.
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To calculate the speed of the blocks after they have moved a distance of 20.0 cm, we need to consider the forces acting on the system and apply Newton's laws of motion. Let's break down the problem step by step:
1. Determine the acceleration of the system:
The acceleration of the system can be found by using the equation for the net force acting on the system. In this case, the only horizontal force is the force of kinetic friction:
Frictional force (f) = coefficient of kinetic friction (μ) x normal force (N)
The normal force is equal to the weight of the upper block (m1) since it is on a horizontal surface:
N = m1 x g
(where g is the acceleration due to gravity)
Next, we can calculate the force of kinetic friction:
f = μ x m1 x g
Since the force of kinetic friction acts in the opposite direction of motion, the net force on the system is:
Net force (Fnet) = m2 x a = m2 x g - f
Solving for 'a', we can find the acceleration of the system.
2. Calculate the time taken to cover the given distance:
We can use the kinematic equation:
s = ut + (1/2) a t^2
Since the initial velocity is zero (the system is at rest), and we need to find the time it takes to cover a distance of 20.0 cm, we can solve for 't'.
3. Calculate the final velocity:
Using the equation:
v = u + a t
(where 'u' is the initial velocity, 'a' is the acceleration, and 't' is the time taken), we can find the final velocity of the system.
Once we have determined the final velocity, we can consider the system as a whole and determine the speed by taking the magnitude of the final velocity vector.
Note: In this case, since the lower block is being pulled downwards, the direction of the velocity is downward. However, the speed is always positive.
It is important to note that the steps provided above are a general guide on how to approach the problem. The actual numerical calculations would require specific values for the masses, acceleration due to gravity, and the coefficient of kinetic friction in order to obtain a specific answer.