Q3: Block of masses M1 and M2 are connected by a light string. The coefficient of friction between M1 and the table surface is 0.30. Determine the acceleration in the block and the tension in the string if M1=4kg and M2=3kg.
Q2: Two 30th weights are suspended at opposite ends of a rope that passes over a light frictionless pulley. The pulley is attached to a chain that goes to the ceiling. (a) What is the tension in the rope? (b) What is the tension in the string?
Q1: A ball of mas 0.15kg slides with negligible friction on a horizontal plane. The ball is attached to a pivot by mean of a string 0.6m long. The ball moves around a circle at 10rev/s. What is the tension in the string?
To determine the acceleration and tension in the system, we need to analyze the forces acting on the blocks.
Let's start by calculating the force of gravity acting on each block:
For block M1:
Force of gravity (Fg1) = M1 * g
where M1 = mass of block M1
g = acceleration due to gravity (approximated as 9.8 meters per second squared)
For block M2:
Force of gravity (Fg2) = M2 * g
where M2 = mass of block M2
g = acceleration due to gravity
Next, let's determine the tension in the string connecting the blocks:
Since the blocks are connected by a light string, the tension force (T) is the same for both blocks. Therefore, Tension (T) is the force that accelerates block M1 and opposes the motion of block M2.
Now, let's analyze the forces on block M1:
1. Force of gravity (Fg1) acts downward.
2. The tension force (T) acts to the right.
3. The frictional force (Ff) acts to the left.
The net force (Fnet1) acting on block M1 is given by:
Fnet1 = T - Ff
Now, let's calculate the frictional force (Ff):
Frictional force (Ff) = coefficient of friction (μ) * normal force (Fn)
The normal force (Fn) is equal to the force of gravity acting on block M1:
Fn = Fg1
The frictional force (Ff):
Ff = μ * Fg1
Similarly, the net force (Fnet2) acting on block M2 is given by:
Fnet2 = Fg2 - T
Now, according to Newton's second law of motion, the net force on each block is equal to the mass of the block multiplied by its acceleration:
For block M1:
Fnet1 = M1 * a
where a = acceleration
For block M2:
Fnet2 = M2 * a
Therefore, we can write the following equations:
T - Ff = M1 * a
Fg2 - T = M2 * a
Now, let's put all the values into the equation and solve for the acceleration:
T - (μ * Fg1) = M1 * a
Fg2 - T = M2 * a
Substituting the values provided in the question:
M1 = 4 kg
M2 = 3 kg
μ = 0.30
Solving these equations simultaneously will give us the value of acceleration (a) and tension (T).