Calculating Forces and Acceleration

[airelemental135]

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.

 

[hotvette]

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.

 

[quicknote]

To calculate the forces and acceleration in these scenarios, we can use Newton's laws of motion and the equations for force and acceleration. In problem 28, we can use the equation F=ma to calculate the horizontal retarding force on the lawn mower, where F is the force, m is the mass, and a is the acceleration. We can then use trigonometry to find the normal force exerted by the ground, as it is equal to the weight of the lawn mower (mg) in the vertical direction. To calculate the force needed to accelerate the lawn mower, we can use the equation F=ma again, where a is the desired acceleration and m is the mass of the lawn mower.

In problem 30, we can use the concept of Newton's third law to determine that the tension in each cord is equal to the weight of the respective bucket, as the buckets are at rest and there is no net force acting on them. However, when the buckets are pulled upward with an acceleration, there will be a net force acting on them, and we can use the equation F=ma to calculate the tension in each cord.

In problem 32, we can use the same equation F=ma to determine the force needed for the window washer to raise herself at a constant speed. To calculate the acceleration when the force is increased by 10%, we can use the equation F=ma again, where F is the increased force and m is the total mass of the window washer and the bucket.