Two movers have to life a refrigerator onto a truck. One of the movers wants to lift the refrigerator vertically, but the other mover wants to roll it up a ramp by applying a force parallel to the ramp. Assume the height of the truck is 1.5 m, the length of the ramp is 5.0 m, and the weight of the refrigerator is 1200 N. Calculate the force and the total work required in each case. Which method is easier?
Now, F=ma, and wouldn't the weight of the fridge be the force required to move it? Then would the force required be the same in each situation?
The vertical work is the same in each case. Figure that. You are neglecting friction on that. Friction is a factor, but so is aching backs from lifting.
The force on the ramp is a classic mechanical wedge (mechanical advantage) problem.
The force is less pushing it up the ramp, IGNORING friction.
I still don't understand how to find the forces. For the force that is on the ramp, do I find vertical force and horizontal force separately?
To find the forces in each situation, let's start by calculating the force required to lift the refrigerator vertically.
When lifting the refrigerator vertically, we need to overcome its weight, which is given as 1200 N. Since the refrigerator is being lifted vertically against gravity, the force required will be equal to its weight. So, in this case, the force required is 1200 N.
Now, let's calculate the force required when rolling the refrigerator up the ramp.
To find the force required, we need to consider the concept of mechanical advantage. In this case, the ramp acts as a simple machine, specifically a inclined plane, which can reduce the force needed to move the object vertically.
The force required to move an object up an inclined plane can be calculated using the formula:
Force = Weight of the object * (Length of the ramp / Height of the ramp)
In this case, the weight of the refrigerator is 1200 N, the length of the ramp is 5.0 m, and the height of the ramp (which is the same as the height of the truck) is 1.5 m.
Plugging in these values into the formula, the force required to move the refrigerator up the ramp is:
Force = 1200 N * (5.0 m / 1.5 m) ≈ 4000 N
So, in this case, the force required to roll the refrigerator up the ramp is approximately 4000 N.
Now, let's compare the total work required in each case.
In the case of lifting the refrigerator vertically, the work done is given by the formula:
Work = Force * Distance
Since the height of the truck is 1.5 m and the refrigerator needs to be lifted vertically, the distance is 1.5 m. Therefore, the work done is:
Work = 1200 N * 1.5 m = 1800 J
In the case of rolling the refrigerator up the ramp, the work done is given by the same formula:
Work = Force * Distance
Since the length of the ramp is 5.0 m and the refrigerator needs to be moved along the ramp, the distance is 5.0 m. So, the work done is:
Work = 4000 N * 5.0 m = 20,000 J
Therefore, the total work required in each case is 1800 J for lifting vertically and 20,000 J for rolling up the ramp.
In terms of which method is easier, the rolling-up-the-ramp method requires less force but more work. This means that while it may be easier to apply less force, the movers would need to exert themselves for a longer distance, potentially leading to more fatigue. Therefore, the ease of the method may vary depending on the mover's capability and preferences.