Question

1. what is the kinetic energy of a 5 kg object moving at 7 m/s?
2. if you throw a 0.4 kg ball at a speed of 20 m/s, what is the ball’s kinetic energy?
3. a car with a mass of 900 kg is travelling at a speed of 25 m/s. what is the kinetic energy of the car?

potential energy $pe_g = mgh$

1. what is the gravitational potential energy of a ceiling fan that has a mass of 7 kg and is 4 m above the ground?

$m=7kg$ $g=9.8 m/s$ $h=4m$
$pe_g=(7)(9.8)(4)=274.4$ (note: original handwritten calculation had a typo, corrected here for accuracy)

1. find the gpe of a coffee mug with a mass of 0.3 kg on a 1-m high counter top:
2. if you have a mass of 80 kg and you are standing on a platform 3 m above the ground, what is your gravitational potential energy?
3. a 2-kg book is moved from a shelf that is 2 m off the ground to a shelf that is 1.5 m off the ground. what is the change in gpe?
4. what is the gravitational potential energy of a diver with a mass of 60 kg who is 10 m above the water?

Explanation:

Kinetic Energy Problems

Kinetic energy formula: $KE = \frac{1}{2}mv^2$, where $m$ = mass, $v$ = speed, $g=9.8\ \text{m/s}^2$ for potential energy.

---

Problem 4 (Kinetic Energy)

Step1: Identify given values

$m=0.4\ \text{kg}$, $v=20\ \text{m/s}$

Step2: Substitute into KE formula

$KE = \frac{1}{2} \times 0.4 \times (20)^2$
$KE = 0.2 \times 400 = 80$

---

Problem 5 (Kinetic Energy)

Step1: Identify given values

$m=900\ \text{kg}$, $v=25\ \text{m/s}$

Step2: Substitute into KE formula

$KE = \frac{1}{2} \times 900 \times (25)^2$
$KE = 450 \times 625 = 281250$

---

Potential Energy Problems

Gravitational Potential Energy formula: $PE_g = mgh$

---

Problem 1 (Potential Energy)

Step1: Identify given values

$m=7\ \text{kg}$, $g=9.8\ \text{m/s}^2$, $h=4\ \text{m}$

Step2: Substitute into GPE formula

$PE_g = 7 \times 9.8 \times 4$
$PE_g = 274.4$

---

Problem 2 (Potential Energy)

Step1: Identify given values

$m=0.3\ \text{kg}$, $g=9.8\ \text{m/s}^2$, $h=1\ \text{m}$

Step2: Substitute into GPE formula

$PE_g = 0.3 \times 9.8 \times 1$
$PE_g = 2.94$

---

Problem 3 (Potential Energy)

Step1: Identify given values

$m=80\ \text{kg}$, $g=9.8\ \text{m/s}^2$, $h=3\ \text{m}$

Step2: Substitute into GPE formula

$PE_g = 80 \times 9.8 \times 3$
$PE_g = 2352$

---

Problem 4 (Potential Energy)

Step1: Calculate initial and final GPE

Initial: $PE_{g1} = 2 \times 9.8 \times 2 = 39.2$
Final: $PE_{g2} = 2 \times 9.8 \times 1.5 = 29.4$

Step2: Find change in GPE

$\Delta PE_g = PE_{g2} - PE_{g1}$
$\Delta PE_g = 29.4 - 39.2 = -9.8$

---

Problem 5 (Potential Energy)

Step1: Identify given values

$m=60\ \text{kg}$, $g=9.8\ \text{m/s}^2$, $h=10\ \text{m}$

Step2: Substitute into GPE formula

$PE_g = 60 \times 9.8 \times 10$
$PE_g = 5880$

Answer:

1. Kinetic Energy (Problem 4): $80\ \text{J}$
2. Kinetic Energy (Problem 5): $281250\ \text{J}$
3. Gravitational Potential Energy (Problem 1): $274.4\ \text{J}$
4. Gravitational Potential Energy (Problem 2): $2.94\ \text{J}$
5. Gravitational Potential Energy (Problem 3): $2352\ \text{J}$
6. Change in Gravitational Potential Energy (Problem 4): $-9.8\ \text{J}$
7. Gravitational Potential Energy (Problem 5): $5880\ \text{J}$