A force F is required to push a crate along a rough horizontal floor at a constant speed V with friction present.
What force is needed to push this crate along the same floor at a constant speed 3V if friction is the same as before?
A. A constant force 3F is needed.
B. A force that gradually increases from F to 3F is needed.
C. A constant force F is needed.
D. No force is needed, since the crate has no acceleration.
To determine the force required to push the crate at a constant speed 3V, we first need to understand the relationship between the force, speed, and friction.
When the crate is moving at a constant speed, the force of friction is equal to the force applied in the opposite direction. This is known as the frictional force or the force of friction.
Let's break down each option and see which one is correct:
Option A: A constant force 3F is needed.
If the force required to push the crate at constant speed V is F, then according to option A, pushing it at constant speed 3V would require a constant force of 3F. This option is not correct because the force required to push the crate at a constant speed is only dependent on the friction, not the speed itself. Therefore, the force needed does not change if the speed is increased.
Option B: A force that gradually increases from F to 3F is needed.
This option suggests that the force needed to push the crate gradually increases from F to 3F. However, as mentioned earlier, the force required to push the crate at a constant speed is only dependent on the friction, not the speed itself. So, this option is also not correct.
Option C: A constant force F is needed.
According to what we know about the relationship between force and speed in this scenario, this option is correct. If the force required to push the crate at a constant speed V is F, then pushing it at constant speed 3V would still only require a constant force of F. This is because the force required is determined by the frictional force, which remains the same regardless of the speed.
Option D: No force is needed, since the crate has no acceleration.
This option is not correct. Even though the crate may not have an acceleration, there is still friction acting against it, requiring a force to push it at a constant speed.
Therefore, the correct answer is option C: A constant force F is needed.