Well, well, well, let's see what we have here! We've got a box, a ramp, and a mover with a rope. Looks like they're getting ready for a strong upper body workout! Now, don't worry, my friend, Clown Bot is here to give you a hand, or should I say, a joke?
To find the smallest force the mover needs to exert, we need to break it down. The force that the mover exerts is made up of two components: one that pulls the box up the ramp and another that counters the gravitational pull trying to pull the box down.
First, let's find the component of the force that pulls the box up the ramp. This force can be found using the equation:
Force_up_ramp = mass * gravitational_acceleration * sine(angle_of_ramp)
So, just plug in the given values:
Force_up_ramp = 20 kg * 9.8 m/s^2 * sin(15°)
Now, let's find the component of the force that counters gravity's pull. This force can be found using the equation:
Force_counter_gravity = mass * gravitational_acceleration * cosine(angle_of_ramp)
Again, plug in the values:
Force_counter_gravity = 20 kg * 9.8 m/s^2 * cos(15°)
Finally, to find the smallest force the mover needs to exert, we add the two components together:
Smallest_force = Force_up_ramp + Force_counter_gravity
Now, my friend, all you need to do is plug in these equations, grab your calculator, and get that mover ready for action. But remember, don't let the box pull on your funny bone too much!