1) Skid and Mitch are pushing on a sofa in opposite directions with forces of 530 N and 370 N respectively. The mass of the sofa is 48 kg. The sofa is initially at rest before it accelerates. There is no friction acting on the sofa. (a) Calculate the acceleration of the sofa. (b) What velocity does the sofa have after it moves 2.5 m? (c) How long does it take to travel 2.5 m?

1) Skid and Mitch are pushing on a sofa in opposite
directions with forces of 530 N and 370 N respectively. The mass of the sofa is 48 kg. The sofa is initially at rest before it accelerates. There is no friction acting on the sofa. (a) Calculate the acceleration of the sofa. (b) What velocity does the sofa have after it moves 2.5 m? (c) How long does it take to travel 2.5 m?
2) You have three force
vectors acting on a mass at the origin. Use the component method we covered in lecture to find the magnitude and direction of the re- sultant force acting on the mass.
3) You have three force
vectors acting on a mass at the origin. Use the component method we covered in lecture to find the magnitude and direction of the re- sultant force acting on the mass.
4) A bowling ball rolls off of a table that is 1.5 m tall. The
ball lands 2.5 m from the base of the table. At what speed did the ball leave the table?
5) Skid throws his guitar up
into the air with a velocity of 45 m/s. Calculate the maximum height that the guitar reaches from the point at which Skid lets go of the guitar. Use energy methods.
6) A beam of mass 12 kg and length 2 m is attached to a
hinge on the left. A box of 80 N is hung from the beam 50 cm from the left end. You hold the beam horizontally with your obviously powerful index finger. With what force do you push up on the beam?
7) The tennis ball of mass 57 g which
you have hung in your garage that lets you know where to stop your car so you don’t crush your garbage cans is entertaining you by swinging in a vertical circle of radius 75 cm. At the bottom of its swing it has a speed of 4 m/s. What is the tension in the string at this point?
Skid MitchSofa
y
F1 = 40 N
45°
F2 = 90 N
35°
x
F3 = 60 N
y
F1 = 45 N60°
F2 = 65 N
8) Derivatives:
a) Given: y = (4x + L)(2×2 – L), find dx dy
.
b) Given:   
  
− +=
Lx2 Lx2lny , find
dx dy
.
9) Integrals:
a) Given: − θ θλ
o
o
45
45 d
r cosk
, evaluate. 50° x
F3 = 85 N
70°
Guitar
Skid
b) Given: ( ) + R
0 2322 dr
xr
kxr2 , evaluate.