Question

color - by - number
name:
hour: date:
directions: solve each problem then color in the answer on the color - by - number
page on the back.
gravitational potential energy
gravitational potential energy = mass x acceleration x height
elastic potential energy =.5 x spring constant x stretch/compression²
mass:4 kg
acceleration: 9.8 m/s²
height: 2 m
potential energy =
mass: 5 kg
acceleration: 9.8 m/s²
height: 10 m
potential energy =
mass:3 kg
acceleration: 9.8 m/s²
height: 5 m
potential energy =
mass:4 kg
acceleration: 9.8 m/s²
height: 10 m
potential energy =
mass:2 kg
acceleration: 9.8 m/s²
height: 5 m
potential energy =
mass:.5 kg
acceleration: 9.8 m/s²
height: 4 m
potential energy =
spring constant: 100 n/m
stretched: 0.3 m
potential energy =
spring constant: 50 n/m
stretched: 0.6 m
potential energy =
spring constant: 200 n/m
stretched: 2 m
potential energy =
spring constant: 75 n/m
compression: 0.4 m
potential energy =
spring constant: 80 n/m
compression: 0.35 m
potential energy =
spring constant: 250 n/m
compression: 1 m
potential energy =

Explanation:

Step1: Calculate gravitational potential energy for first set

Use formula \(PE = m\times a\times h\). For \(m = 4\space kg\), \(a=9.8\space m/s^{2}\), \(h = 2\space m\), \(PE=4\times9.8\times2 = 78.4\space J\)

Step2: Calculate gravitational potential energy for second set

For \(m = 5\space kg\), \(a = 9.8\space m/s^{2}\), \(h = 10\space m\), \(PE=5\times9.8\times10=490\space J\)

Step3: Calculate gravitational potential energy for third set

For \(m = 3\space kg\), \(a = 9.8\space m/s^{2}\), \(h = 5\space m\), \(PE=3\times9.8\times5 = 147\space J\)

Step4: Calculate gravitational potential energy for fourth set

For \(m = 4\space kg\), \(a = 9.8\space m/s^{2}\), \(h = 10\space m\), \(PE=4\times9.8\times10 = 392\space J\)

Step5: Calculate gravitational potential energy for fifth set

For \(m = 2\space kg\), \(a = 9.8\space m/s^{2}\), \(h = 5\space m\), \(PE=2\times9.8\times5=98\space J\)

Step6: Calculate gravitational potential energy for sixth set

For \(m = 0.5\space kg\), \(a = 9.8\space m/s^{2}\), \(h = 4\space m\), \(PE=0.5\times9.8\times4 = 19.6\space J\)

Step7: Calculate elastic potential energy for seventh set

Use formula \(PE=\frac{1}{2}kx^{2}\). For \(k = 100\space N/m\), \(x = 0.3\space m\), \(PE=\frac{1}{2}\times100\times(0.3)^{2}=4.5\space J\)

Step8: Calculate elastic potential energy for eighth set

For \(k = 50\space N/m\), \(x = 0.6\space m\), \(PE=\frac{1}{2}\times50\times(0.6)^{2}=9\space J\)

Step9: Calculate elastic potential energy for ninth set

For \(k = 200\space N/m\), \(x = 2\space m\), \(PE=\frac{1}{2}\times200\times(2)^{2}=400\space J\)

Step10: Calculate elastic potential energy for tenth set

For \(k = 75\space N/m\), \(x = 0.4\space m\), \(PE=\frac{1}{2}\times75\times(0.4)^{2}=6\space J\)

Step11: Calculate elastic potential energy for eleventh set

For \(k = 80\space N/m\), \(x = 0.35\space m\), \(PE=\frac{1}{2}\times80\times(0.35)^{2}=4.9\space J\)

Step12: Calculate elastic potential energy for twelfth set

For \(k = 250\space N/m\), \(x = 1\space m\), \(PE=\frac{1}{2}\times250\times(1)^{2}=125\space J\)

Answer:

78.4 J, 490 J, 147 J, 392 J, 98 J, 19.6 J, 4.5 J, 9 J, 400 J, 6 J, 4.9 J, 125 J