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G-Force worksheet

Grades 11–12

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Find the g-force from: Turn or loop
- Speed: 100 km/h
- Radius of the turn: 52 m
Find: G-force
Answer
2.
Problem 2.
- Find the g-force from: Known acceleration
- Acceleration (a): 26 m/s²
Find: G-force
Answer
3.
Problem 3.
- Find the g-force from: Speed change over time
- Starting speed: 0 km/h
- Final speed: 74 km/h
- Time taken: 3 s
Find: G-force
Answer
4.
Problem 4.
- Find the g-force from: Stopping distance
- Speed: 105 km/h
- Stopping distance: 48 m
Find: G-force
Answer
5.
Problem 5.
- Find the g-force from: Turn or loop
- Speed: 130 km/h
- Radius of the turn: 46 m
Find: G-force
Answer
6.
Problem 6.
- Find the g-force from: Speed change over time
- Starting speed: 0 km/h
- Final speed: 100 km/h
- Time taken: 2 s
Find: G-force
Answer
7.
Problem 7.
- Find the g-force from: Speed change over time
- Starting speed: 0 km/h
- Final speed: 125 km/h
- Time taken: 4 s
Find: G-force
Answer
8.
Problem 8.
- Find the g-force from: Known acceleration
- Acceleration (a): 35 m/s²
Find: G-force
Answer
9.
Problem 9.
- Find the g-force from: Known acceleration
- Acceleration (a): 32 m/s²
Find: G-force
Answer
10.
Problem 10.
- Find the g-force from: Turn or loop
- Speed: 110 km/h
- Radius of the turn: 50 m
Find: G-force
Answer

Answer key: G-Force worksheet

1. G-force: 1.51 g
1. Change the speed to m/s, the standard unit the formula uses (1 km/h = 0.277777777778 m/s)
  $100 km/h \times 0.277777777778$ $= 27.777778 m/s$
2. Turning keeps changing your direction, which is an acceleration toward the center. Square the speed v and divide by the turn radius r
  $\frac{{27.777778}^{2}}{52}$ $= 14.838557 m/s²$
3. Divide the size of the acceleration by standard gravity (9.80665 m/s²) to see how many g it is
  $\frac{14.838557}{9.80665}$ $= 1.513112 g$
2. G-force: 2.65 g
1. Use the acceleration you entered
  $a$ $= 26 m/s²$
2. Divide the size of the acceleration by standard gravity (9.80665 m/s²) to see how many g it is
  $\frac{26}{9.80665}$ $= 2.651262 g$
3. G-force: 0.7 g
1. Change the starting speed to m/s, the standard unit the formula uses (1 km/h = 0.277777777778 m/s)
  $0 km/h \times 0.277777777778$ $= 0 m/s$
2. Change the final speed to m/s, the standard unit the formula uses (1 km/h = 0.277777777778 m/s)
  $74 km/h \times 0.277777777778$ $= 20.555556 m/s$
3. Find the acceleration: how much the speed changed, divided by how long it took
  $\frac{20.555556 - 0}{3}$ $= 6.851852 m/s²$
4. Divide the size of the acceleration by standard gravity (9.80665 m/s²) to see how many g it is
  $\frac{6.851852}{9.80665}$ $= 0.698694 g$
4. G-force: 0.9 g
1. Change the speed to m/s, the standard unit the formula uses (1 km/h = 0.277777777778 m/s)
  $105 km/h \times 0.277777777778$ $= 29.166667 m/s$
2. For steady braking, square the speed v and divide by twice the stopping distance d
  $\frac{{29.166667}^{2}}{2 \times 48}$ $= 8.8614 m/s²$
3. Divide the size of the acceleration by standard gravity (9.80665 m/s²) to see how many g it is
  $\frac{8.8614}{9.80665}$ $= 0.903611 g$
5. G-force: 2.89 g
1. Change the speed to m/s, the standard unit the formula uses (1 km/h = 0.277777777778 m/s)
  $130 km/h \times 0.277777777778$ $= 36.111111 m/s$
2. Turning keeps changing your direction, which is an acceleration toward the center. Square the speed v and divide by the turn radius r
  $\frac{{36.111111}^{2}}{46}$ $= 28.348094 m/s²$
3. Divide the size of the acceleration by standard gravity (9.80665 m/s²) to see how many g it is
  $\frac{28.348094}{9.80665}$ $= 2.890701 g$
6. G-force: 1.42 g
1. Change the starting speed to m/s, the standard unit the formula uses (1 km/h = 0.277777777778 m/s)
  $0 km/h \times 0.277777777778$ $= 0 m/s$
2. Change the final speed to m/s, the standard unit the formula uses (1 km/h = 0.277777777778 m/s)
  $100 km/h \times 0.277777777778$ $= 27.777778 m/s$
3. Find the acceleration: how much the speed changed, divided by how long it took
  $\frac{27.777778 - 0}{2}$ $= 13.888889 m/s²$
4. Divide the size of the acceleration by standard gravity (9.80665 m/s²) to see how many g it is
  $\frac{13.888889}{9.80665}$ $= 1.416273 g$
7. G-force: 0.89 g
1. Change the starting speed to m/s, the standard unit the formula uses (1 km/h = 0.277777777778 m/s)
  $0 km/h \times 0.277777777778$ $= 0 m/s$
2. Change the final speed to m/s, the standard unit the formula uses (1 km/h = 0.277777777778 m/s)
  $125 km/h \times 0.277777777778$ $= 34.722222 m/s$
3. Find the acceleration: how much the speed changed, divided by how long it took
  $\frac{34.722222 - 0}{4}$ $= 8.680556 m/s²$
4. Divide the size of the acceleration by standard gravity (9.80665 m/s²) to see how many g it is
  $\frac{8.680556}{9.80665}$ $= 0.88517 g$
8. G-force: 3.57 g
1. Use the acceleration you entered
  $a$ $= 35 m/s²$
2. Divide the size of the acceleration by standard gravity (9.80665 m/s²) to see how many g it is
  $\frac{35}{9.80665}$ $= 3.569007 g$
9. G-force: 3.26 g
1. Use the acceleration you entered
  $a$ $= 32 m/s²$
2. Divide the size of the acceleration by standard gravity (9.80665 m/s²) to see how many g it is
  $\frac{32}{9.80665}$ $= 3.263092 g$
10. G-force: 1.9 g
1. Change the speed to m/s, the standard unit the formula uses (1 km/h = 0.277777777778 m/s)
  $110 km/h \times 0.277777777778$ $= 30.555556 m/s$
2. Turning keeps changing your direction, which is an acceleration toward the center. Square the speed v and divide by the turn radius r
  $\frac{{30.555556}^{2}}{50}$ $= 18.67284 m/s²$
3. Divide the size of the acceleration by standard gravity (9.80665 m/s²) to see how many g it is
  $\frac{18.67284}{9.80665}$ $= 1.9041 g$