Two boxes with different masses M1 = 1.8 kg and M2 = 2.6 kg are tied together on a frictionless ramp surface which makes an angle θ = 21° with the horizontal (see the figure below).
What is the tension in the rope connecting the two boxes? N
What is the tension in the rope connecting the first box to the ramp? N
To find the tension in the rope connecting the two boxes, we can consider the forces acting on the system. The only force acting along the ramp is the component of the weight of the boxes parallel to the ramp surface. This force can be calculated using the formula:
Force parallel to ramp = Mass × Gravity × sin(θ)
For box M1, the force parallel to the ramp is given by:
Force1 = M1 × g × sin(θ)
For box M2, the force parallel to the ramp is given by:
Force2 = M2 × g × sin(θ)
Since the tension in the rope is the same for both boxes, we can equate the two forces and solve for the tension:
Tension = Force1 = Force2 = M1 × g × sin(θ) = M2 × g × sin(θ)
To find the tension in the rope connecting the first box to the ramp, we need to consider the forces acting on box M1. Along the ramp, the only force acting on box M1 is the component of its weight parallel to the ramp, which is given by:
Force1 = M1 × g × sin(θ)
Therefore, the tension in the rope connecting the first box to the ramp is equal to the force acting along the ramp on box M1. This tension can be found by using the formula:
Tension = Force1 = M1 × g × sin(θ)
Substituting the given values for M1, θ, and g into the equation will give you the answer in newtons (N).