in the drawing, a block of mass m1 and m2 =6.7kg are connected by a massless rope over a pulley. the smooth incline surface makes an angle of 42 with the horizontal, and the block on the incline is the block of the mass m2. find the mass m1 of the hanging block that will cause the system to be in equilibrium

Question

in the drawing, a block of mass m1 and m2 =6.7kg are connected by a massless rope over a pulley. the smooth incline surface makes an angle of 42 with the horizontal, and the block on the incline is the block of the mass m2. find the mass m1 of the hanging block that will cause the system to be in equilibrium

Answer 1

In equilibrium, the tension (T) in the rope should balance the gravitational force acting on the hanging block (m1g), and the component of gravitational force acting on the incline block (m2g*sin(θ)) should balance the tension (T) in the rope as well. Mathematically, this can be written as:

T = m1 * g
T = m2 * g * sin(θ)

Combining both equations, we get:

m1 * g = m2 * g * sin(θ)

We're given m2 = 6.7 kg and θ = 42°. The acceleration due to gravity (g) is 9.81 m/s². We can find the mass m1 of the hanging block:

m1 = m2 * sin(θ)
m1 = 6.7 kg * sin(42°)
m1 = 6.7 kg * 0.6691 (rounded sin(42°) value)
m1 ≈ 4.483 kg

So, the mass m1 of the hanging block that will cause the system to be in equilibrium is approximately 4.483 kg.

In equilibrium, the tension (T) in the rope should balance the gravitational force acting on the hanging block (m1*g), and the component of gravitational force acting on the incline block (m2*g*sin(θ)) should balance the tension (T) in the rope as well. Mathematically, this can be written as:

In equilibrium, the tension (T) in the rope should balance the gravitational force acting on the hanging block (m1g), and the component of gravitational force acting on the incline block (m2g*sin(θ)) should balance the tension (T) in the rope as well. Mathematically, this can be written as: