Question

A skater is on an ice rink. His right skate has an area of 6.8 cm2 in contact with the ice, but his left skate only has 4 cm2 in contact with the ice.
With his right foot he exerts a pressure on the ice of 50 N/cm2.
He applies an equal force with his left foot.
What is the pressure exerted by his left foot in N/cm2?

Answer 1

Given :

• A skater is on a ice rink. His right skate has an area of 6.8 cm² in contact with the ice, but his left skate has only 4 cm² .With his right foot he exerts a pressure of 50 N/cm² on the ice. He applies equal force with the both foot.

$\rule{200pt}{3pt}$

To Find :

• Pressure exerted by his left foot.

$\rule{200pt}{3pt}$

Solution :

$\color{orange}{✪}$How to Solve :

As given in the question he is applying equal force on the both foot. So, first we will calculate the force applied on the right foot by using the formula for Pressure. After that, we can easily calculate the pressure exerted by the left foot. Let's Solve :

$\qquad{━━━━━━━━━━━━━━━━━━━━━}$

$\color{orange}{✪}$Formula Used :

$\large{\color{cyan}{\bigstar}} \: \: {\underline{\boxed{\color{red}{\pmb{\sf{ Pressure = \dfrac{Force}{ Area} }}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━}$

$\color{orange}{✪}$Calculating the Force applied on right foot :

Here we have :

• ➳ Pressure = 50 N / cm²
• ➳ Area = 6.8 cm²
• ➳ Force = ?

Calculation Starts :

${\longmapsto{\qquad{\sf{ Pressure{\small_{(First \: Foot )}} = \dfrac{Force }{ Area} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ 50 = \dfrac{Force}{6.8} }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Force = 50 \times 6.8 }}}} \\ \\ \ {\qquad{\textsf{ Force applied by first foot = {\pink{\sf{ 340 \: N}}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━}$

$\color{orange}{✪}$Calculating the Pressure on left foot :

Here we have :

• ➳ Pressure = ?
• ➳ Force = 340 N
• ➳ Area = 4 cm²

Calculation Starts :

${\longmapsto{\qquad{\sf{ Pressure = \dfrac{Force}{ Area}}}}} \\ \\ \ {\longmapsto{\qquad{\sf{ Pressure{\small_{(Second \: Foot )}} = \cancel\dfrac{340}{ 4} }}}} \\ \\ \ {\qquad{\textsf{ Pressure on second foot = {\purple{\sf{ 85 \: N / cm² }}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━}$

$\color{orange}{✪}$Therefore :

❝ Pressure on the left foot is 85 N/cm² .❞

$\\ {\underline{\rule{300pt}{9pt}}}$