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Machines - Forces and the Mechanics of Motion

Grade 8IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Work is defined as the product of the force applied to an object and the displacement of the object in the direction of the force, measured in Joules (JJ).

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A machine is a device that changes the magnitude or direction of a force to make work easier.

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Mechanical Advantage (MAMA) is a measure of how much a machine multiplies the input effort; it is the ratio of Load (LL) to Effort (EE).

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Velocity Ratio (VRVR) is the ratio of the distance moved by the effort (dEd_E) to the distance moved by the load (dLd_L).

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Efficiency (η\eta) represents how much of the input work is converted into useful output work. Real machines always have an efficiency less than 100%100\% due to friction.

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Levers are categorized into three classes based on the relative positions of the Fulcrum, Load, and Effort: First Class (Fulcrum in middle), Second Class (Load in middle), and Third Class (Effort in middle).

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The Law of Moments states that for a system in equilibrium, the sum of clockwise moments about a pivot equals the sum of anticlockwise moments: F1×d1=F2×d2F_1 \times d_1 = F_2 \times d_2.

📐Formulae

W=F×dW = F \times d

P=WtP = \frac{W}{t}

MA=Load (L)Effort (E)MA = \frac{\text{Load (L)}}{\text{Effort (E)}}

VR=dEdLVR = \frac{d_E}{d_L}

η=(Work OutputWork Input)×100%\eta = \left( \frac{\text{Work Output}}{\text{Work Input}} \right) \times 100\%

η=MAVR×100%\eta = \frac{MA}{VR} \times 100\%

Moment=F×d⊥\text{Moment} = F \times d_{\perp}

💡Examples

Problem 1:

A crowbar is used to lift a rock weighing 600 N600\,N. If an effort of 150 N150\,N is applied, what is the Mechanical Advantage (MAMA) of the crowbar?

Solution:

Given L=600 NL = 600\,N and E=150 NE = 150\,N. MA=LE=600150=4MA = \frac{L}{E} = \frac{600}{150} = 4

Explanation:

The Mechanical Advantage is 44, meaning the machine multiplies the input force by 44 times.

Problem 2:

In a pulley system, the effort moves 10 m10\,m to lift a load by 2 m2\,m. If the MAMA is 44, calculate the efficiency of the system.

Solution:

Step 1: Calculate Velocity Ratio (VRVR): VR=dEdL=102=5VR = \frac{d_E}{d_L} = \frac{10}{2} = 5 Step 2: Calculate Efficiency (η\eta): η=MAVR×100%=45×100%=80%\eta = \frac{MA}{VR} \times 100\% = \frac{4}{5} \times 100\% = 80\%

Explanation:

The efficiency is 80%80\%, which implies that 20%20\% of the energy is lost, likely to friction or the weight of the pulleys.

Problem 3:

A student exerts a force of 50 N50\,N to push a box 4 m4\,m across a floor in 5 seconds5\,seconds. Calculate the power exerted.

Solution:

Step 1: Work done (WW): W=F×d=50×4=200 JW = F \times d = 50 \times 4 = 200\,J Step 2: Power (PP): P=Wt=2005=40 WP = \frac{W}{t} = \frac{200}{5} = 40\,W

Explanation:

The student performs 200 J200\,J of work, and since it is done over 5 s5\,s, the rate of doing work (Power) is 4040 Watts (WW).