In the figure we see two blocks connected by a string and tied to a wall, with θ = 27°. The mass of the lower block is m = 1.2 kg; the mass of the upper block is 2.0 kg.
To answer this question, we need to apply some principles from physics, specifically the concept of forces and equilibrium. The figure you mentioned seems to depict a simple pulley system with two blocks and a string.
The first step is to identify the forces acting on the system. Since the figure mentions a string, we can assume that tension forces are present. There are two tension forces acting on the system, one in the upward direction and one in the downward direction.
Next, we need to consider the forces due to gravity. Both blocks will experience a downward force due to their respective masses. The force due to gravity can be calculated using the equation F = m * g, where F is the force, m is the mass, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
In this case, the downward force on the lower block can be calculated as F1 = m1 * g, where m1 is the mass of the lower block (1.2 kg). Similarly, the downward force on the upper block can be calculated as F2 = m2 * g, where m2 is the mass of the upper block (2.0 kg).
Since the two blocks are connected by a string, the tension force acting on the lower block is the same as the upward tension force acting on the upper block (assuming an idealized, frictionless system). We can denote this tension force as T.
Now, let's consider the vertical direction. The net force in the vertical direction should be equal to zero since the system is at rest (equilibrium). This means that the sum of the upward and downward forces should be equal.
In the vertical direction, we have the following forces:
- Tension force on the lower block (acting upward)
- Force due to gravity on the lower block (acting downward)
- Force due to gravity on the upper block (acting downward)
Mathematically, we can write the equilibrium equation as:
T - F1 - F2 = 0
Now, we need to use the given angle θ = 27°. By drawing a free-body diagram, we can see that Tension (T) can be split into two components: one in the vertical direction and one in the horizontal direction.
The vertical component of tension, Tv, can be calculated as Tv = T * sin(θ), and the horizontal component, Th, can be calculated as Th = T * cos(θ).
Since we are interested in the vertical forces, we can substitute T with Tv in the equilibrium equation:
Tv - F1 - F2 = 0
Now, we can substitute Tv with T * sin(θ):
T * sin(θ) - F1 - F2 = 0
Substituting the expressions for F1 and F2, we have:
T * sin(θ) - m1 * g - m2 * g = 0
Now, we can solve this equation to find the tension force (T) in the string. Since we have all the given values (m1 = 1.2 kg, m2 = 2.0 kg, θ = 27°, g = 9.8 m/s^2), we can plug them into the equation and calculate T.
T * sin(27°) - (1.2 kg) * (9.8 m/s^2) - (2.0 kg) * (9.8 m/s^2) = 0
Solving this equation will give us the value of T, which represents the tension force in the string.