Question

A roller coaster car is going over the top of a 18-m-radius circular rise. at the top of the hill, the passengers "feel light," with an apparent weight only 50 % of their true weight.

Answer 1

The solution for this problem is:

If they feel 50% of their weight that means that the centripetal force is also 50% of their weight 1g - 0.5g = 0.5g 

Then 0.5* 9.8m/s² * 18m = 88.2 would be v² 

Then get the square root, the answer would be:
and v = 9.391 m/s is the answer.

Answer 2

The speed of roller coaster car is about 9.4 m/s

$\texttt{ }$

Further explanation

Centripetal Acceleration can be formulated as follows:

$\large {\boxed {a = \frac{ v^2 } { R } }$

a = Centripetal Acceleration ( m/s² )

v = Tangential Speed of Particle ( m/s )

R = Radius of Circular Motion ( m )

$\texttt{ }$

Centripetal Force can be formulated as follows:

$\large {\boxed {F = m \frac{ v^2 } { R } }$

F = Centripetal Force ( m/s² )

m = mass of Particle ( kg )

v = Tangential Speed of Particle ( m/s )

R = Radius of Circular Motion ( m )

Let us now tackle the problem !

$\texttt{ }$

Complete Question:

A roller coaster car is going over the top of a 18-m-radius circular rise. at the top of the hill, the passengers "feel light," with an apparent weight only 50% of their true weight. How fast is the coaster moving?

Given:

radius of circular motion = R = 18 m

weight of passengers = w

apparent weight of passengers = N = 50%w

Asked:

speed of roller coaster car = v = ?

Solution:

$\Sigma F = m \frac{v^2}{R}$

$w - N = m \frac{v^2}{R}$

$w - 50\% w = m \frac{v^2}{R}$

$50\% w = m \frac{v^2}{R}$

$50\% mg = m \frac{v^2}{R}$

$\frac{1}{2} g = \frac{v^2}{R}$

$v^2 = \frac{1}{2} gR$

$v = \sqrt { \frac{1}{2} g R }$

$v = \sqrt { \frac{1}{2} \times 9.8 \times 18}$

$v = \frac{21}{5} \sqrt{5} \texttt{ m/s}$

$\boxed{v \approx 9.4 \texttt{ m/s}}$

$\texttt{ }$

Learn more

• Impacts of Gravity : brainly.com/question/5330244
• Effect of Earth’s Gravity on Objects : brainly.com/question/8844454
• The Acceleration Due To Gravity : brainly.com/question/4189441

$\texttt{ }$

Answer details

Grade: High School

Subject: Physics

Chapter: Circular Motion