Physics: Magnitude of force & acceleration

For the following questions, the answers are given but I need the workings to arrive at the answer.

1. A force acts on a 1.5 kg, mass, giving it an acceleration of 3.0 m/s^2. (a) If the same force acts on a 2.5 kg mass, what acceleration would be produced? (b) What is the magnitude of force?
Answer: (a) 1.8m/s^2 (b) 4.5 N

2. An object (mass 10 kg) slides upward on a slippery vertical wall. A force F of 60 N acts at an angle of 60*. (a) Determine the normal force exerted on the object by the wall. (b) Determine the objects acceleration.
Answer: (a) 30N (b) -4.60 m/s^2

3. During a daring rescue, a helicopter rescue squad initially accelerates a little girl (mass 25 kg) vertically off the roof of a burning building. They do this by dropping a rope down to her, which she holds on to as they pull her up. Neglect the mass of the rope. (a) What force causes the girl to accelerate vertically upward (1) her weight; (2) the pull of the helicopter on the rope (4) the pull of the rope on the girl
(b) Determine the pull of the rope (tension) if she initially accelerates upwards at 0.750 m/s^2.
Answer: (a)The correct answer is 4th option, the pull of the rope on girl (b) 264N

4. The weight of the 500 kg object is 4900 N. (a) When the object is on a moving elevator, its measure weight could be (1) zero. (2) between zero to 4900N (3) more than 4900N, (4) all of the preceeding. WHY? (b) Describe the motion if the objects measured weight is only 4000N in a moving elevator.
Answer: (a) N is the measure weight and can take any value, depending on acceleration. Thus 4th option. (b) The elevator must be accelerating downward at 1.8 m/s^2.

5. A girl pushes a 25 kg lawn mower. If F=30N and @ = 37*. (a)What is the acceleration of the mower? (b) What is the normal force exerted on the mower by the lawn? Ignore friction.
Answer: (a) 4.96 m/s^2 (b) 2.6 x 10^2 N