Math Problem Statement

Use the formula W = fd to find the work done for the given values of force (f) and distance (d) in exercises 1-6, and use other formulas to find unknowns in exercises 7-9.

Solution

Let's solve the exercises provided step-by-step.

Exercises 1-6

The formula given is W=fdW = f \cdot d, where:

  • ff is the force,
  • dd is the distance,
  • WW is the work done.

Let's compute WW for each exercise.

  1. f=30f = 30, d=20d = 20 W=30×20=600W = 30 \times 20 = 600

  2. f=17f = 17, d=9d = 9 W=17×9=153W = 17 \times 9 = 153

  3. f=1125f = 1125, d=10d = 10 W=1125×10=11250W = 1125 \times 10 = 11250

  4. f=203f = 203, d=27d = 27 W=203×27=5481W = 203 \times 27 = 5481

  5. f=176f = 176, d=326d = 326 W=176×326=57376W = 176 \times 326 = 57376

  6. f=2400f = 2400, d=120d = 120 W=2400×120=288000W = 2400 \times 120 = 288000

Exercises 7-9

These questions use formulas from page 19, where likely each formula corresponds to physical relationships involving mass, acceleration, voltage, resistance, etc. Let's assume the following standard formulas commonly used in physics:

  1. Force (F = m * a) for Exercise 7.
  2. Power (P = V * I), where V=IRV = I \cdot R, so rearranged for P=V2/RP = V^2 / R for Exercise 8.
  3. Current (I = V / R) for Exercise 9.

Solving Each:

  1. If m=1600m = 1600 and a=24a = 24, find ff. f=m×a=1600×24=38400f = m \times a = 1600 \times 24 = 38400

  2. If V=120V = 120 and R=24R = 24, find PP. P=V2R=120224=1440024=600P = \frac{V^2}{R} = \frac{120^2}{24} = \frac{14400}{24} = 600

  3. If E=120E = 120 and R=15R = 15, find II. I=ER=12015=8I = \frac{E}{R} = \frac{120}{15} = 8

Would you like further details on any specific exercise?

Additional Questions for Practice

  1. If f=50f = 50 and d=30d = 30, what is the work WW done?
  2. Given m=2000m = 2000 and a=15a = 15, find the force ff.
  3. If V=240V = 240 and R=30R = 30, calculate the power PP.
  4. Suppose E=150E = 150 and R=10R = 10; find the current II.
  5. If the force doubles but the distance remains constant, how does that affect WW?

Tip

When calculating work, remember that it's always the product of force and distance. Units are essential: force in Newtons (N) and distance in meters (m) yield work in Joules (J).

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Math Problem Analysis

Mathematical Concepts

Work and Energy
Force and Motion
Electric Power and Current

Formulas

Work done (W) = f * d
Force (F) = m * a
Power (P) = V^2 / R
Current (I) = V / R

Theorems

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Suitable Grade Level

Grades 9-10