How Do I Solve These Complex Newtonian Force Problems?

[TripelS]

Help needed in Bunch of Newton/Force Problems!

So we went over these questions in school,... and I was absent.. So my teacher expects me to self-teach myself. But I have trouble with these specific questions (out of 50 questions )...

Please show me steps

Question 1:
A mass of 25 kg is acted on by two forces: F1 is 15 N due east, and F2 is 10 N due north. The acceleration of the mass is

A. 0.72 m/s2, 56.3° north of east.
B. 0.20 m/s2, east.
C. 0.72 m/s2, 33.7° north of east.
D. 1.0 m/s2, 33.7° north of east.
E. 0.20 m/s2, 56.3° north of east.

Question 2:

An astronaut lands on an earthlike planet and drops a small lead ball with a mass of 76.5 g from top of her spaceship. The point of release is 18 m above the surface of the planet and the ball takes 2.5 s to reach the ground. The astronaut's mass on Earth is 68.5 kg. Her weight on the planet is

A. 69 N
B. 395 N
C. 670 N
D. 990 N
E. 1.02 kNQuestion 5:

A lamp with a mass 42.6 kg is hanging from wires as shown. The tension T1 in the Vertical wire is
A. 210 N
B. 417 N
C. 570 N
D. 360 N
E. 730 NQuestion 6:

A lamp with a mass M is suspended from the ceiling by two cords as shown. The ratio of the magnitude of the vertical component of the tension in T2 to that in T3 is

A. 1:1
B. 1:2
C. 2:3
D. 3:2
E. 3:1

Question 7:

A vertical rope is attached to an object that has a mass of 40.0 kg and is at rest. The tension in the rope needed to give the object an upward speed of 3.50 m/s in 0.700 s is

A. 592 N
B. 392 N
C. 200 N
D. 980 N
E. 729 NQuestion 8:

A 6 kg block sitting on a smooth table is connected to a free-hanging 2 kg mass by a stretchless, massless cord that passes over a small frictionless pulley. The acceleration of the two-block system is

A. g
B.(1/2)g
C. (1/3)g
D. (1/4)g
E. (2/3)g

Question 9:

A 15 kg block sitting on a smooth table is connected to a free-hanging 5 kg mass by a stretchless, massless cord that passes over a small frictionless pulley. The acceleration of the two-block system is

A. g
B. (1/2)g
C. (1/3)g
D. (1/4)g
E. zeroQuestion 10:

Two tug-of-war teams are pulling on the ends of a rope, each team with a force of 1000 N. If the rope does not move, the tension in the rope is

A. 2000 N
B. 500 N
C. 1000 N
D. zero
E. 2000 kg

 

[CompuChip]

Question 1: What is the total force (as a vector?) What are its magnitude and direction?

Question 2: Try s = 1/2 g t^2 (and remember that formula!)

Question 5: Dissolve the gravitational force in the directions of the cables. The lamp does not accelerate, what does this tell you about the magnitude of T?

Question 6: Probably similar to the other ones, but I'd need to see the diagram.

Question 7: Use F = ma. What is the net force needed? How does this force relate to the tension T?

Questions 8, 9: draw force diagrams. How do the pulleys transfer gravitational force to the block (doubling, canceling, ...)?

Question 10: Draw a free body diagram for the rope.