Some force problems

1. Sep 26, 2008

musicfairy

Here's a couple of multiple choice problems that deal with force, friction, and the like. I need someone to check my answers. Of course, I checked them, but my reasoning could be wrong.

For 1 & 2

A block of mass 3 kg, initially at rest, is pulled along a frictionless, horizontal surface with a force shown as a function of time t by the graph above.

1. The acceleration of the block at t = 2 s is
(A) 3/4 m/s2
(B) 4/3 m/s2
(C) 2 m/s2
(D) 8 m/s2
(E) 12 m/s2

2. The speed of the block at t = 2s is
(A) 4/3 m/s
(B) 8/3 m/s
(C) 4 m/s
(D) 8 m/s
(E) 24 m/s

how I got it: a = (2t)/3, v = t2/3, v(2) = 4/3

For 3.

3. An object weighing 300 N is suspended by means of two cords, as shown above. The tension in the horizontal cord is
(A) 0N
(B) 150N
(C) 210N
(D) 300N
(E) 400N

My answer: D because it's 45 degrees, so the x and y components are equal.

For 4, 5 & 6

4. Which figure best represents the free-body diagram for the box if it is accelerating up the ramp?
(A) Figure A
(B) Figure B
(C) Figure C
(D) Figure D
(E) Figure E

5. Which figure best represents the free-body diagram for the box if it is at rest on the ramp?
(A) Figure A
(B) Figure B
(C) Figure C
(D) Figure D
(E) Figure E

6. Which figure best represents the free-body diagram for the box if it is sliding down the ramp at constant speed?
(A) Figure A
(B) Figure B
(C) Figure C
(D) Figure D
(E) Figure E

7. Two blocks of masses M and m, with M > m, are connected by a light string. The string passes over a frictionless pulley of negligible mass so that the blocks hang vertically. The blocks are then released from rest. What is the acceleration of the block of mass M?

A) g
B) (M - m)g/M
C) (M + m)g/M
D)(M + m)g/(M - m)
E) (M - m)g/(M + m)

Mg - mg = (M + m)a
a = (M - m)g / (M + m)

8. A horizontal force F pushes a block of mass m against a vertical wall. The coefficient of friction between the block and the wall is μ. What value of F is necessary to keep the block from slipping down the wall?
(A) mg
(B) μmg
(C) mg /μ
(D) mg(1 - μ)
(E) mg(1 + μ)