Final answer:
The tension required for the block to start moving is approximately 10.14 N.
Step-by-step explanation:
To find the tension required for the block to start moving, we can first calculate the gravitational force acting on the block. The gravitational force can be calculated using the formula:
Fg = mg
where Fg is the gravitational force, m is the mass of the block, and g is the acceleration due to gravity. In this case, the mass of the block is 4.00 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.
Fg = (4.00 kg)(9.8 m/s^2) = 39.2 N
The force required to overcome static friction and start the block moving is equal to the maximum static friction force. The formula for static friction is:
Fstatic = μs * Fn
where Fstatic is the maximum static friction force, μs is the coefficient of static friction, and Fn is the normal force. The normal force can be calculated using:
Fn = m * g * cosθ
where θ is the angle of the incline. In this case, θ = 30.0°.
Fn = (4.00 kg)(9.8 m/s^2)(cos30.0°) = 33.8 N
Finally, we can calculate the maximum static friction force:
Fstatic = (0.300)(33.8 N) = 10.14 N
Therefore, the tension required for the block to start moving is approximately 10.14 N.