Answer to Question #305946 in Mechanics | Relativity for Yna

Question

Solve the following problems completely and present your final answers in two (2) decimal places.

1. The rear wheel of a 150 kg tricycle accidentally ran over a nail. The circular tip of the nail has a diameter of 0.001 m.How much pressure did the wheel of the tricycle experience assuming that the entire weight of the tricycle is concentrated on the rear wheel that ran over the nail.
2. A medium sized car typically weighs 1000 kg.

A hydraulic system to jack the car up above an inspection pit hasfour slave cylinderswhose pistons have a cross section area of 0.01 m². The cross-section area of the master cylinder piston is 0.00125 m².

(a) What is the weight of the car?

(b) What is the minimum force that must be applied to the master cylinder to raise the car upwards?

Answer 1

Explanations & Calculations

1)

$\qquad\qquad \begin{aligned} \small P&=\small \frac{F}{A}=\frac{150\,kg\times9.8\,ms^{-2}}{\pi(0.001\,m)^2\times0.25}\\ &=\small 1.87\times10^9\,Pa \end{aligned}$

2)

a)

$\qquad\qquad \begin{aligned} \small W&=\small mg=1000\,kg\times9.8\,ms^{-2}=9800.00\,N \end{aligned}$

b)

• Pressure applied on a single slave cylinder is one-quarter of the total weight which is $\small 250\times9.8\,N$ .
• Since the pressure is equal on each cylinder,

$\qquad\qquad \begin{aligned} \small \frac{250\times9.8}{0.01\,m^2}&=\small \frac{F}{0.00125\,m^2}\\ \small F&=\small 306.25\,N\,(\equiv32.25\,kg)) \end{aligned}$