Calculating Forces and Acceleration

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To solve the problems presented, one should start by applying Newton's laws of motion, particularly F=MA, and creating free body diagrams to visualize the forces involved. For question 28, the horizontal retarding force can be calculated using the applied force and the angle of the handle, while the normal force requires considering the weight of the mower and the vertical component of the applied force. In question 30, the tension in the cords can be determined by analyzing the forces acting on each bucket at rest and under acceleration. Question 32 involves calculating the force needed to maintain constant speed and the resulting acceleration when that force is increased. Understanding these fundamental principles is crucial for accurately solving the problems.
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Does anyone know how I can do 28, 30, and 32, reproduced below?

28. A person pushes a 14.5-kg lawn mower at constant speed with a force of 88.0 N directed along the handle, which is at an angle of 45.0 degrees to the horizontal. Calculate (a) the horizontal retarding force on the mower, then (b) the normal force exerted vertically upward on the mower by the ground, and (c) the force the person must exert on the lawn mower to accelerate it from rest to 1.5 m/s in 2.5 seconds (assuming the same retarding force).

30. One 3.0-kg paint bucket is haning by a massless cord from another 3.0-kg paint bucket, also hanging by a massless cord. (a) If the buckets are at rest, what is the tension in each cord? (b) If the two buckets are pulled upward with an acceleration of 1.60 m/s^2 by the upper cord, calculate the tension in each cord.

32. A window washer pulls herself upward using the bucket-pulley apparatus. (a) How hard must she pull downward to raise herself slowly at constant speed? (b) If she increases this force by 10 percent, what will her acceleration be? The mass of the person plus the bucket is 65 kg.
 
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What have you tried so far? On problems like this, it is always best to draw a free body diagram with the forces, sum them up and use good ol' F=MA.
 
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