Question

An elevator is descending with uniform acceleration. To measure the acceleration, a person in the elevator drops a coin at the moment the elevator starts. The coin is 6 ft above the floor of the elevator at the time it is dropped. The person observes that the coin strikes the floor in 1 second. Calculate from these data the acceleration of the elevator.

Answer 1

Answer:

Explanation:

Let acceleration of lift be a.

acceleration of ball with respect to the lift = acceleration of ball with respesct to ground - acceleration of the lift

Or, aball(lift) = g - a = 9.8 m/s^2 - a = 32 ft./s^2 - a [ 9.8m = 32 ft. ]

displacement s = 6 ft.

time taken t = 1 s.

initial velocity u = 0

s = ut + 1/2 at^2 = 0*1 + 1/2 (32-a)*1*1 = 1/2 (32-a)

Therefore, 6 = 1/2 (32-a)

Hence a = 20 ft./s^2

Answer 2

The acceleration of the elevator is,

a = 20.33ft/s².

Explanation:

Step 1:

Given values

For an elevator and coin :

                               $S_{c}=s coin$ Initial velocity = u = 0 m/s

As the elevator descends, the coin has to move more distance than 1.8 cm to strike the floor with a uniform acceleration "a"

                       Time (t) = 1 sec

                        $s_{c}=u t+\frac{1}{2} a t^{2}$          

                        $s_{c}=0 \times 1+\frac{1}{2} a . 1^{2}$

                        $s_{c}=0+\frac{1}{2} a \times 1$

                        $s_{c}=\frac{1}{2} a$  

                          a = g    

                         $s_{c}=\frac{z}{2}$

Step 2:      

The cumulative distance travelled by coin shall be indicated as :

                       $1.8+\frac{a}{2}=\frac{1}{2}$

                           $\frac{26+a}{2}=\frac{7}{2}$

                        $3.6+a=g$

                        $3.6+a=9.8$

                        $a=9.8-3.6$

                        $a=6.2 \mathrm{m} / \mathrm{s}^{2}$

Acceleration in feet (multiply by 3.28)                                                                      $a=6.2 \times 3.28=20.33 \mathrm{ft} / \mathrm{s}^{2}$

Thus, the acceleration is, a = 20.33ft/s².