Handwritten solutions to physics problems on mechanical advantage and work, showing step-by-step calculations.

Let’s go through each problem one by one, step by step. I’ll explain everything clearly so you can follow along easily.

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Problem 1:

We’re told that an input force of 200 N is applied to a wheelbarrow with a mechanical advantage (MA) of 2.2. We need to find the output force.

Mechanical Advantage formula:
> MA = Output Force / Input Force

So we rearrange it to solve for Output Force:
> Output Force = MA × Input Force

Plug in the numbers:
> Output Force = 2.2 × 200 N
> Output Force = 440 N

✔ So the output force is 440 Newtons.

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Problem 2:

You want to move a sail from a boat using a block and tackle system. The load (output force) is 715 N, and your input force is only 65 N. What’s the mechanical advantage?

Again, use:
> MA = Output Force / Input Force

> MA = 715 N / 65 N
> MA = 11

✔ Mechanical Advantage is 11.

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Problem 3:

A lever has an input arm of 3 meters and an output arm of 0.75 meters. What’s the mechanical advantage?

For levers, mechanical advantage is:
> MA = Length of Input Arm / Length of Output Arm

> MA = 3 m / 0.75 m
> MA = 4

✔ Mechanical Advantage is 4.

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Problem 4:

Same lever as above — input arm = 3 m, output arm = 0.75 m. If you push down on the input end with a force of 80 N, what’s the output force?

Use:
> Output Force = MA × Input Force
> Output Force = 4 × 80 N
> Output Force = 320 N

✔ Output force is 320 Newtons.

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Problem 5:

A ramp is used to lift a heavy box into a truck. The ramp is 3 meters long and rises 0.5 meters high. What’s the ideal mechanical advantage?

For ramps (inclined planes), ideal mechanical advantage is:
> IMA = Length of Ramp / Height of Ramp

> IMA = 3 m / 0.5 m
> IMA = 6

✔ Ideal Mechanical Advantage is 6.

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Problem 6:

Using the same ramp (IMA = 6), if you apply an input force of 100 N, what’s the theoretical output force? (Assume no friction.)

> Output Force = IMA × Input Force
> Output Force = 6 × 100 N
> Output Force = 600 N

✔ Theoretical output force is 600 Newtons.

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Problem 7:

A pulley system lifts a 200 N weight. You pull with 50 N of force. What’s the actual mechanical advantage?

> AMA = Output Force / Input Force
> AMA = 200 N / 50 N
> AMA = 4

✔ Actual Mechanical Advantage is 4.

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Problem 8:

In Problem 7, if the rope you pull moves 4 meters, how far does the weight rise?

Remember: In simple machines, work input ≈ work output (ignoring friction).

Work = Force × Distance

So:
> Input Work = Output Work
> (Input Force) × (Input Distance) = (Output Force) × (Output Distance)

Plug in known values:
> 50 N × 4 m = 200 N × d_out
> 200 = 200 × d_out
> d_out = 200 / 200 = 1 meter

✔ The weight rises 1 meter.

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Problem 9:

A gear system has a driving gear with 10 teeth and a driven gear with 30 teeth. What’s the mechanical advantage?

For gears:
> MA = Number of Teeth on Driven Gear / Number of Teeth on Driving Gear

> MA = 30 / 10 = 3

✔ Mechanical Advantage is 3.

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Problem 10:

If the driving gear in Problem 9 turns at 60 RPM, how fast does the driven gear turn?

Gears are inversely related — bigger gear turns slower.

> Speed of Driven Gear = (Teeth on Driving Gear / Teeth on Driven Gear) × Speed of Driving Gear

> Speed_driven = (10 / 30) × 60 RPM
> Speed_driven = (1/3) × 60 = 20 RPM

✔ Driven gear turns at 20 RPM.

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Final Answer:

1. 440 N
2. 11
3. 4
4. 320 N
5. 6
6. 600 N
7. 4
8. 1 meter
9. 3
10. 20 RPM