A 600 lb. oak packing crate is sitting on a cross grained, 14 ft long, oak ramp.
The force of the box against the ramp is
520 lbs, and the downhill force on the box
is 300 lbs.
Will the box slide down the hill all by itself?
Give the box a nudge, will it stop?
If the box will slide down the hill by
itself, what will be the acceleration on
the box?
Two big guys push on the box with a combined force of 300 lbs. How long will
it take for them to push the box down the ramp?
The two guys push the wrong box down the hill, and have to push it back up.
How much force does it take to get the box moving?
How much to keep it moving?
To determine whether the box will slide down the hill all by itself, we need to compare the forces acting on the box. The force pushing the box downhill is 300 lbs, while the force against the ramp is 520 lbs. Since the force against the ramp is greater than the downhill force, the box will not slide down by itself.
However, if the box is given a nudge, it will eventually stop due to the opposing forces. We can calculate the acceleration of the box to determine how quickly it will stop. The net force acting on the box is the difference between the force pushing it downhill (300 lbs) and the force against the ramp (520 lbs), which is -220 lbs (opposite in direction).
To find the acceleration, we can use Newton's second law of motion, which states that acceleration (a) is equal to the net force (F_net) divided by the mass (m) of the object. The mass of the box is given as 600 lbs. Since the weight of an object is equivalent to its mass times the acceleration due to gravity (which is approximately 32 ft/s^2), we can convert the weight of the box to mass as follows:
Mass = Weight / Acceleration due to Gravity
Mass = 600 lbs / 32 ft/s^2
The acceleration can then be calculated as follows:
Acceleration (a) = Net Force (F_net) / Mass (m)
To find the force required to move the box, we need to overcome the static friction between the box and the ramp. Once the box is in motion, the force required to keep it moving is the kinetic friction between the box and the ramp. The magnitude of the frictional force can be calculated using the coefficient of friction (μ) and the normal force (N).
Given that the force required to move the box is the static friction and the force required to keep it moving is the kinetic friction, we need to determine the normal force on the box first. The normal force is equal to the weight of the box (600 lbs), as the box is sitting on a flat surface (the ramp) which exerts an equal and opposite force.
Now, let's address each question one by one:
1. Will the box slide down the hill all by itself?
No, the box will not slide down the hill by itself because the force against the ramp is greater than the downhill force.
2. Give the box a nudge, will it stop?
Yes, if the box is given a nudge, it will eventually stop due to the opposing forces. We can calculate the acceleration to determine how quickly it will come to a stop using Newton's second law.
3. If the box will slide down the hill by itself, what will be the acceleration on the box?
Since the box will not slide down the hill by itself, there is no acceleration to calculate in this case.
4. Two big guys push on the box with a combined force of 300 lbs.
To determine how long it will take for them to push the box down the ramp, we need to consider the net force applied to the box. The net force is the combined force of the two guys (300 lbs) plus the downhill force (300 lbs) minus the force against the ramp (520 lbs). This gives us a net force of 80 lbs. Using Newton's second law, we can calculate the acceleration with this net force and the mass of the box (600 lbs). Then we can calculate the time using the equation: Time (t) = Final Velocity (v) / Acceleration (a).
5. How much force does it take to get the box moving?
The force required to get the box moving is equal to the static friction between the box and the ramp. It is the same as the force against the ramp, which is 520 lbs.
6. How much force to keep it moving?
The force required to keep the box moving is equal to the kinetic friction between the box and the ramp. This force can be calculated using the coefficient of friction (μ) and the normal force (N) exerted on the box. Since the normal force is equal to the weight of the box (600 lbs), we can multiply it by the coefficient of kinetic friction to find the force required to keep it moving.