Question

Suppose you have a 150-kg wooden crate resting on a wood floor. (a) what maximum force (in n) can you exert horizontally on the crate without moving it?

Answer 1

Missing detail:
The coefficient of static friction is not specified in the problem. Searching online, I found that for wood-on-wood contact it is between 0.25-0.5. I assume here the maximum value, 0.5.

Solution:
When pushing the crate horizontally with a force F, only two forces act horizontally on the crate: F and
`F_f`, the frictional force, which points into the opposite direction of F and whose magnitude is given by

`F_f = \mu_S m g`
where
`\mu_S=0.5` is the coefficient of static friction,
`m=150 kg` is the mass of the crate and
`g=9.81 m/s^2` is the gravitational acceleration.

In order to start to move the crate, the force F applied must overcome the frictional force. This means that the minimum value of F necessary is equal to Ff:

`F_(min)=F_f = \mu_S mg=(0.5)(150 kg)(9.81 m/s^2)=735.7 N`