Question

A roller coaster is towed up an incline at a steady speed of 0.4800 m/s by a chain parallel to the surface of the incline. The slope is 2.900%, which means that the elevation increases by 2.900 m for every 100.0 m of distance along the surface. The mass of the roller coaster is 402.3 kg. Neglecting friction, what is the magnitude of the force exerted on the roller coaster by the chain?

Answer 1

The force exerted by the chain is 117N

Step-by-step explanation:

We have to draw a free body diagram to visualize this problem better.

according to Newton's second law:

`\sum F=m*a`

but the roller coaster is having a constant speed so:

`\sum F=0`

`F_c-F_(mg)=0`

`F_c=F_(mg)`

`F_(mg)=m*g*sin(\theta)\\\\\theta=arctg((2.9m)/(100m))=1.7^o\\\\F_(mg)=402.3kg*9.81m/s*sin(1.7^o)\\F_(mg)=117N`

So:

`F_c=117N`