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Answer :
Final answer:
The minimum tension necessary to start the crate moving at the optimum angle is 0.45 * 116 kg * 9.8 m/s^2.
Explanation:
To find the minimum tension necessary to start the crate moving at the optimum angle, we need to consider the forces acting on the crate and the angle at which the tension force is applied.
The force of static friction opposes any force applied to move the crate. The maximum force of static friction can be calculated using the equation F_static = μ_s * N, where F_static is the force of static friction, μ_s is the coefficient of static friction, and N is the normal force.
The normal force is equal to the weight of the crate, which can be calculated using the equation N = m * g, where m is the mass of the crate and g is the acceleration due to gravity.
Since the crate is at rest, the force of static friction must be equal to the tension force applied to the crate. Therefore, we can set up the equation F_static = T, where T is the tension force.
Substituting the equations for F_static and N, we get μ_s * m * g = T.
To find the minimum tension necessary to start the crate moving at the optimum angle, we need to find the maximum value of the tension force. This occurs when the angle between the tension force and the horizontal floor is 90 degrees, resulting in the maximum possible force of static friction.
Therefore, the minimum tension necessary to start the crate moving at the optimum angle is μ_s * m * g.
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