Physics for Life Sciences Summary

Lecture 1: Kinematics
• Speed
o Average speed
∆𝑥 3 𝜇𝑚
▪ 𝑣𝑎𝑣𝑔 = 𝑡
= 70 𝑠
≈ 40 𝑛𝑚⁄𝑠
o Position x(t) with constant speed v
∆𝑥
▪ 𝑣= ∆𝑡
→ 𝑥(𝑡) = 𝑥0 + 𝑣 ∙ 𝑡
▪ If v is not constant
𝜕𝑥
𝑣= 𝜕𝑡
o Speed v(t) with constant acceleration a
∆𝑣
▪ 𝑎= → 𝑣(𝑡) = 𝑣0 + 𝑎𝑡
∆𝑡
▪ If a is not constant
𝜕𝑣
𝑎= 𝜕𝑡
o The speed changes with an acceleration so
𝑣(𝑡) = 𝑣0 + 𝑎𝑡 can’t be substituted into 𝑥(𝑡) =
𝑥0 + 𝑣𝑡
o Inconstant speed
(𝑥(𝑡)𝑖𝑠 𝑡ℎ𝑒 𝑝𝑟𝑖𝑚𝑖𝑡𝑖𝑣𝑒 𝑜𝑓 𝑣(𝑡))
▪ 𝑥(𝑡) = ∫ 𝑣(𝑡) 𝑑𝑡 = ∫(𝑣𝑜 + 𝑎𝑡) 𝑑𝑡
1
▪ 𝑥(𝑡) = 𝑥0 + 𝑣0 ∙ 𝑡 + 𝑎𝑡 2
2
𝑣−𝑣0
𝑡=
𝑎
𝑣 2 = 𝑣02 + 2𝑎 ∙ (𝑥 − 𝑥0 )
𝑣−𝑣0
𝑎=
𝑡
𝑣0 +𝑣
𝑥 = 𝑥0 + ( )∙𝑡
2
𝑣 +𝑣
→ 𝑣𝑎𝑣𝑔 = 0
2
o Projectile Motion
▪ X-axis
𝑣
cos(𝜃0 ) = 𝑣𝑥0 → 𝑣𝑥0 = 𝑣0 ∙ cos(𝜃0 )
0
𝑎𝑥 (𝑡) = 0
𝑣𝑥 (𝑡) = 𝑣𝑥0
𝑥(𝑡) = 𝑥0 + 𝑣𝑥0 ∙ 𝑡
▪ Y-axis
𝑣𝑦0
sin(𝜃0 ) = 𝑣0
→ 𝑣𝑦0 = 𝑣0 ∙ sin(𝜃0 )
𝑎𝑦 (𝑡) = −𝑔
𝑣𝑦 (𝑡) = 𝑣𝑦0 − 𝑔𝑡
1
𝑦(𝑡) = 𝑦0 + 𝑣𝑦0 ∙ 𝑡 − 2 𝑔 ∙ 𝑡 2




1

, Lecture 2: Forces
• Newton’s First Law
o If an object is not subjected to a net force, the speed will remain constant.
▪ Acceleration is zero
• Newton’s Second Law
o The net force on an object is the product of the mass and the acceleration.
o 𝐹⃗ = 𝑚 ∙ 𝑎⃗
• Newton’s Third Law
o If an object A subjects a force on object B, then object B subjects object A to an
equal, but opposite, force.
• Gravity
o ⃗⃗⃗⃗
𝐹𝑧 = 𝑤
⃗⃗⃗
o 𝑤 =𝑚∙𝑔
▪ 𝐵𝑊 = 𝐵𝑜𝑑𝑦 𝑊𝑒𝑖𝑔ℎ𝑡 → 𝐹𝑜𝑟𝑐𝑒 𝑜𝑓 𝐺𝑟𝑎𝑣𝑖𝑡𝑦 𝑜𝑛 𝐵𝑜𝑑𝑦
• Gravitation
𝐺∙𝑚1 ∙𝑚2
o 𝐹𝐺 = 𝑟2
▪ 𝐺 = 𝑔𝑟𝑎𝑣𝑖𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 ≈ 6.673 ∙ 10−11 𝑁 ∙ 𝑚2 /𝑘𝑔2
▪ 𝑚1 𝑎𝑛𝑑 𝑚2 𝑎𝑟𝑒 𝑡ℎ𝑒 𝑚𝑎𝑠𝑠𝑒𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑤𝑜 𝑜𝑏𝑗𝑒𝑐𝑡𝑠
▪ 𝑟 𝑖𝑠 𝑡ℎ𝑒 𝑑𝑖𝑠𝑐𝑡𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑡ℎ𝑒 𝑡𝑤𝑜 𝑜𝑏𝑗𝑒𝑐𝑡𝑠
▪ Gravity and Gravitational force are equal on the surface of a planet.
𝐺∙𝑚𝑜𝑏𝑗𝑒𝑐𝑡 ∙𝑚𝑒𝑎𝑟𝑡ℎ
𝑚𝑜𝑏𝑗𝑒𝑐𝑡 ∙ 𝑔 = 𝑟2
𝐺∙𝑚𝑒𝑎𝑟𝑡ℎ
𝑔= 𝑟2
• Normal Force ⃗⃗⃗⃗⃗
𝐹𝑁
o If there is no acceleration despite gravity, there has to be an opposite force
o ⃗⃗⃗⃗
𝐹𝑦 = 𝑁 − 𝑤 = 0
• ⃗⃗
Tension Force 𝑇




o 𝐹𝑝 = 𝑇𝑥
▪ 𝐹𝑝 = 𝑇 ∙ sin 30°
o 𝑤 = 𝑇𝑦
▪ 𝑤 = 𝑇 ∙ cos 30°
𝐹 𝑤
o 𝑇 = sin 𝑝30° & 𝑇 = cos 30°
𝐹𝑝 𝑤
o sin 30°
= cos 30°
sin 30° 1
o 𝐹𝑝 = 𝑤 ∙ cos 30° = 200 ∙ 3 √3 ≈ 115 𝑁

2