Question
A ramp 20 m long and 4 m high is used to lift a heavy box. A pulley system with 4 rope sections supporting the load is used to lift an identical box to a height of 4 m.
If friction is ignored, the ramp requires a _____ to lift the load.
smaller input distance and a greater force
greater input distance and a smaller force
smaller input distance and a smaller force
greater input distance and a greater force
If friction is ignored, the ramp requires a _____ to lift the load.
smaller input distance and a greater force
greater input distance and a smaller force
smaller input distance and a smaller force
greater input distance and a greater force
Answers
GPT-4o mini
To analyze the situation, we can apply the concepts of mechanical advantage and work in both scenarios (the ramp and the pulley system).
### Ramp:
1. **Height of the ramp (Height of load lifted)**: 4 m
2. **Length of ramp (Input distance)**: 20 m
The work done against gravity when lifting the load using the ramp is equal to the gravitational potential energy gained by the load. The force required to lift the load using the ramp is less than the weight of the load because the length of the ramp is greater than the height.
### Pulley System:
1. **Height lifted**: 4 m
2. **Rope sections**: 4
The mechanical advantage of a pulley system with 4 rope sections is 4. This means that the input force required is one-fourth of the weight of the load, and the distance pulled will be 4 times the height lifted when considering the entire movement.
### Comparison:
- **Ramp**: Greater input distance (20 m) with a smaller force than the weight of the load.
- **Pulley System**: Smaller input distance and a smaller force compared to lifting the box directly.
Thus, without friction, the ramp requires a **greater input distance and a smaller force** to lift the load compared to lifting it directly.
**Answer: greater input distance and a smaller force.**
### Ramp:
1. **Height of the ramp (Height of load lifted)**: 4 m
2. **Length of ramp (Input distance)**: 20 m
The work done against gravity when lifting the load using the ramp is equal to the gravitational potential energy gained by the load. The force required to lift the load using the ramp is less than the weight of the load because the length of the ramp is greater than the height.
### Pulley System:
1. **Height lifted**: 4 m
2. **Rope sections**: 4
The mechanical advantage of a pulley system with 4 rope sections is 4. This means that the input force required is one-fourth of the weight of the load, and the distance pulled will be 4 times the height lifted when considering the entire movement.
### Comparison:
- **Ramp**: Greater input distance (20 m) with a smaller force than the weight of the load.
- **Pulley System**: Smaller input distance and a smaller force compared to lifting the box directly.
Thus, without friction, the ramp requires a **greater input distance and a smaller force** to lift the load compared to lifting it directly.
**Answer: greater input distance and a smaller force.**