To find the acceleration experienced by the two blocks, we can use Newton's second law of motion. The net force acting on each block is the component of the force of gravity parallel to the ramp, which can be calculated using the equation:
F_parallel = m * g * sin(θ),
where m is the mass of each block, g is the acceleration due to gravity, and θ is the angle of the ramp.
Since both blocks are connected by a string, the magnitude of the tension in the string will be the same for both blocks and can be considered as the net force acting on each block.
Now, we can write the equations for the acceleration of each block and the tension in the string:
Acceleration of block 1:
m1 * a = m1 * g * sin(θ)
a = g * sin(θ)
Acceleration of block 2:
m2 * a = m2 * g * sin(θ)
a = g * sin(θ) * (m1 / m2)
Now, let's substitute the given values into the equation to find the acceleration of each block:
- Acceleration of block 1:
a1 = 9.8 m/s^2 * sin(36°)≈ 5.94 m/s^2
- Acceleration of block 2:
a2 = 9.8 m/s^2 * sin(36°) * (3.7 kg / 16.2 kg) ≈ 1.36 m/s^2
To find the tension in the rope, we can use block 2 as a reference:
Tension in string = m2 * a2 * g
Substituting the given values, we have:
Tension = 16.2 kg * 1.36 m/s^2 * 9.8 m/s^2 ≈ 222.84 N
Therefore, the tension in the rope is approximately 222.84 Newtons.