After running three trials with a fan cart which has a mass

After running three trials with a fan cart, which has a mass of 480 g, on a horizontal track you have collected the following data:

Acceleration from x-t graph (m/s2 ) 0.642 0.622 0.651

Acceleration from v-t graph (m/s2 ) 0.618 0.664 0.604

120 g is added to the cart and it is placed at rest on a track inclined at 4.5 degrees . The fan is set to push the cart up the incline. Will the cart accelerate up the incline, down the incline, or remain at rest? Explain fully.

Solution

>> On this Inclined Plane, weight of cart is acting downwards.

>> Component of it down the inclined plane, F\" = W*sin(4.5)

As, W = mg

, where , m = Total Mass = 480 + 120 = 600 g

=> F\" = mg*sin(4.5)

=> F\" = 0.77*m

>> Now, force applied by fan on the cart up the inclined plane = ma

, where, a = acceleration provided in several readings.

and, F= ma

>> Now in all readings of acceleration, maximum value of a , a_max = 0.664 m/s² , which is less than 0.77

So, F < F\"

,i.e., force down the inclined plane is more as compared to force up the inclined plane...

>> So, Cart wll accelerate down the incined plane ....... ANSWER...