The provided solution addresses two questions: 2.4.3 Calculate the maximum force that is exerted on the load…

Question

The provided solution addresses two questions: 2.4.3 Calculate the maximum force that is exerted on the load by piston B. 2.4.4 Calculate the distance travelled by piston B.

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Here are the answers to the remaining questions:

Assumption: The areas of the pistons for question 2.4 are $A_A = 10 \, \text{cm}^2$ and $A_B = 50 \, \text{cm}^2$ , as provided in the full context of question 2.4 from the previous image.

2.4.3 Calculate the maximum force that is exerted on the load by piston B.

State the given values.
Input force $F_A = 100 \, \text{N}$
Area of piston A $A_A = 10 \, \text{cm}^2$
Area of piston B $A_B = 50 \, \text{cm}^2$
Apply Pascal's principle.
Pressure is transmitted equally throughout the fluid:
$P_A = P_B$ $\frac{F_A}{A_A} = \frac{F_B}{A_B}$
Solve for the output force $F_B$ .
$F_B = F_A \times \frac{A_B}{A_A}$ $F_B = 100 \, \text{N} \times \frac{50 \, \text{cm}^2}{10 \, \text{cm}^2}$ $F_B = 100 \, \text{N} \times 5$ $F_B = 500 \, \text{N}$
The maximum force exerted on the load by piston B is $\boxed{\text{500 N}}$ .

2.4.4 Calculate the distance travelled by piston B.
State the known values.
Input force $F_A = 100 \, \text{N}$
Input distance $d_A = 10 \, \text{cm}$
Output force $F_B = 500 \, \text{N}$ (from 2.4.3)
Apply the principle of work done (Work input = Work output).
$W_A = W_B$ $F_A \times d_A = F_B \times d_B$
Solve for the output distance $d_B$ .
$d_B = \frac{F_A \times d_A}{F_B}$ $d_B = \frac{100 \, \text{N} \times 10 \, \text{cm}}{500 \, \text{N}}$ $d_B = \frac{1000 \, \text{N} \cdot \text{cm}}{500 \, \text{N}}$ $d_B = 2 \, \text{cm}$
The distance travelled by piston B is $\boxed{\text{2 cm}}$ .

2.4.5 Calculate the mechanical advantage of the system.
State the known values.
Input force $F_A = 100 \, \text{N}$
Output force $F_B = 500 \, \text{N}$ (from 2.4.3)
Area of piston A $A_A = 10 \, \text{cm}^2$
Area of piston B $A_B = 50 \, \text{cm}^2$
Calculate mechanical advantage (MA) using forces or areas.
$MA = \frac{\text{Output Force}}{\text{Input Force}} = \frac{F_B}{F_A}$ $MA = \frac{500 \, \text{N}}{100 \, \text{N}}$ $MA = 5$
Alternatively, using areas:
$MA = \frac{\text{Area of Output Piston}}{\text{Area of Input Piston}} = \frac{A_B}{A_A}$ $MA = \frac{50 \, \text{cm}^2}{10 \, \text{cm}^2}$ $MA = 5$
The mechanical advantage of the system is $\boxed{5}$ .

2.5 Name the type of mechanical advantage that is achieved when a small syringe drives a larger syringe.
The type of mechanical advantage achieved is force multiplication.

The provided solution addresses two questions: 2.4.3 Calculate the maximum force that is exerted on the load by piston B. 2.4.4 Calculate the distance travelled by piston B.

Answer

Step-by-step solution

State the given values.

Apply Pascal's principle.

Solve for the output force $F_B$ .

State the known values.

Apply the principle of work done (Work input = Work output).

Solve for the output distance $d_B$ .

State the known values.

Calculate mechanical advantage (MA) using forces or areas.

Try one yourself

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More Physics Questions

The provided solution addresses two questions: 2.4.3 Calculate the maximum force that is exerted on the load by piston B. 2.4.4 Calculate the distance travelled by piston B.

Answer

Step-by-step solution

State the given values.

Apply Pascal's principle.

Solve for the output force FBF_BFB​.

State the known values.

Apply the principle of work done (Work input = Work output).

Solve for the output distance dBd_BdB​.

State the known values.

Calculate mechanical advantage (MA) using forces or areas.

Try one yourself

Still stuck on this one?

More Physics Questions

Solve for the output force $F_B$ .

Solve for the output distance $d_B$ .