Three blocks are located on a horizontal table. The coefficient of kinetic friction between the blocks and the table is 0.276. They are connected by a massless cord, as shown in the figure below, and pulled to the right. The masses of the three blocks are = 9.0 kg, = 0.5 kg, and = 5.0 kg. The pulling force is equal to = 82.0 N. What is the tension ?
You don't provide or explain the figure. Are there cords between each block? Which cord to you want the tension of? Any cord that is being pulled with 82 N force has that same tension.
there is a cord connecting all three blocks
Tension is 82N if that's the driving force on the first block
To find the tension in the cord, we can start by considering the forces acting on each block separately.
1. For the first block with mass m1 = 9.0 kg:
- There is a tension force T acting to the right.
- There is a friction force f1 acting to the left due to the coefficient of kinetic friction.
2. For the second block with mass m2 = 0.5 kg:
- There is a tension force T acting to the right.
- There is a friction force f2 acting to the left due to the coefficient of kinetic friction.
3. For the third block with mass m3 = 5.0 kg:
- There is a tension force T acting to the right.
- There is a friction force f3 acting to the left due to the coefficient of kinetic friction.
Now, let's find the magnitudes of the friction forces:
The formula for the friction force is given by: f = μN, where μ is the coefficient of friction and N is the normal force.
Since the blocks are on a horizontal table, the normal forces on each block are equal to their weights:
N1 = m1 * g
N2 = m2 * g
N3 = m3 * g
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Now, let's find the magnitudes of the friction forces:
f1 = μ * N1
f2 = μ * N2
f3 = μ * N3
Next, let's find the net force acting on each block:
For the first block:
- The net force is the difference between the tension force and the friction force: T - f1.
For the second block:
- The net force is the difference between the tension force and the friction force: T - f2.
For the third block:
- The net force is the difference between the tension force and the friction force: T - f3.
Now, let's apply Newton's second law (F = ma) to each block:
For the first block:
T - f1 = m1 * a1
For the second block:
T - f2 = m2 * a2
For the third block:
T - f3 = m3 * a3
Since the blocks are connected by a massless cord, they have the same acceleration, so a1 = a2 = a3 = a.
Now, let's substitute the values and solve for T:
Using the given values:
m1 = 9.0 kg
m2 = 0.5 kg
m3 = 5.0 kg
μ = 0.276 (coefficient of kinetic friction)
g ≈ 9.8 m/s^2
F = 82.0 N (pulling force)
Calculate the normal forces:
N1 = m1 * g
N2 = m2 * g
N3 = m3 * g
Calculate the friction forces:
f1 = μ * N1
f2 = μ * N2
f3 = μ * N3
Now, solve the system of equations:
(T - f1) = m1 * a
(T - f2) = m2 * a
(T - f3) = m3 * a
Substitute the calculated values and solve for T.