Q46E - University Physics with Modern Physics

Question

A small car with mass 0.800kg travels at constant speed on the inside of a track that is a vertical circle with radius 5.00m (Fig. E5.45). If the normal force exerted by the track on the car when it is at the top of the track (point B) is 6.00N , what is the normal force on the car when it is at the bottom of the track (point A)?

                               

Step-by-Step Solution

Answer

21.68N

Step 1: Identification of given data

Mass of car is  m = 0.8kg

Radius of track is r = 5.00m

Normal force on car at point B is  $N_B=6N$

Step 2: Significance of centripetal force and centrifugal force

The force applied to an item in curved motion that is pointed toward the axis of rotation or the centre of curvature is known as a centripetal force.

A fictitious force that moves in a circle and is directed away from the centre of the circle is called centrifugal force.

So the centrifugal force use the same formula of centripetal force but in negative sign

$F_c=-\frac{m{v}^2}{r}$

Where, m is mass of body, v is velocity of body and r is radius of circular path

Step 3: Determining the normal force on the car when it is at the bottom of the track (point A)

A car is moving on a circular path so that a centrifugal force act in outward direction to the car.

                                                       

Equating the forces at force at point B

$F_c=N_B+mg$                                                                                                                 …(i)

Now take the point A and equating the forces

$N_A=mg+F_c$                                                                                                                

From equation (i)

$$\begin{gathered} N_A=mg+N_B+mg \\ {N}_A=2mg+N_B \end{gathered}$$

Substitute all the values in above equation  

$$\begin{gathered} N_A=\left(2\times 0.8kg\times 9.8m/s\right)+6N \\ =21.68N \end{gathered}$$

Hence the normal force on the car when it is at the bottom of the track (point A) is 21.68N