Question

If you had a 20 m ramp to push that 120 N object up the same height of 5 m
(neglecting friction), how much force would be needed?​

Answer 1

Given:

A 20 m ramp to push that 120 N object up the same height of 5 m.

To find:

Force required (neglecting friction) ?

Calculation:

So, this is a case of object being pushed upwards along an inclined plane whose inclination can be calculated as follows:

$\therefore \: \sin( \theta) = \dfrac{height}{hypotenuse}$

$\implies \: \sin( \theta) = \dfrac{5}{20}$

$\implies \: \sin( \theta) = \dfrac{1}{4} \: \: \: \: .........(1)$

Now, on an inclined plane , an object experiences a force of $mg\sin(\theta)$ downwards along the plane.

So, at critical conditions, a minimum of $mg\sin(\theta)$ force has to be provided in order to push the body upwards.

$\therefore \: F = mg \sin( \theta)$

$\implies \: F = 120 \times \dfrac{1}{4}$

$\implies \: F = 30 \: N$

So, a force > 30 N can push the object upwards along the inclined plane.