Final answer:
The minimum force required to move a block from rest is determined by the static friction formula, which is the coefficient of static friction times the normal force. For a block on ice with known mass and static friction coefficient, calculate the minimum force by multiplying these values. After the block is moving, its acceleration is determined by applying Newton's second law and subtracting the force of kinetic friction.
Step-by-step explanation:
To calculate the minimum force, fmin, that must be applied to get a block moving from rest, you need to consider static friction, which opposes the start of motion. The minimum force required to overcome static friction and initiate movement is equal to the coefficient of static friction, μ, times the normal force, N. The normal force is typically equal to the gravitational force for an object resting on a horizontal surface, which is the mass of the object, M, times the acceleration due to gravity, g. Therefore, the expression for the minimum force is fmin = μ × M × g. For a block with a mass of 45.0 kg and a coefficient of static friction on ice, the calculation would be fmin = μ × 45.0 kg × 9.81 m/s².
Once the block starts moving, to find its acceleration, you can apply Newton's second law, F = M × a, where F is the force applied, M is the mass, and a is the acceleration. However, now you have to consider kinetic friction if applicable. So the force that contributes to acceleration is the applied force minus the force of kinetic friction (μk × N). Thus, the acceleration a can be found using a = (F - μk × M × g) / M.