A cart is pulled a distance D on a flat, horizontal surface by a constant force F that acts at an angle θ with the horizontal direction. The other forces on the object during this time are gravity (Fw), normal forces (FN1) and (FN2), and rolling frictions (Fr1) and (Fr2) as shown below. What is the work done by each force? (Use any variable or symbol stated above as necessary, where the subscript w is lowercase in Fw.)

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A cart is pulled a distance D on a flat, horizontal surface by a constant force F that acts at an angle θ with the horizontal direction. The other forces on the object during this time are gravity (Fw), normal forces (FN1) and (FN2), and rolling frictions (Fr1) and (Fr2) as shown below. What is the work done by each force? (Use any variable or symbol stated above as necessary, where the subscript w is lowercase in Fw.)
The image illustrates the forces acting on a box that is placed on wheels and situated on a horizontal surface. Here's a detailed breakdown of the diagram:

1. **Box on Wheels**: The box is shown resting on two wheels, indicating that it can move along the surface.

2. **Forces Acting on the Box**:
   - **\(\vec{F}_N1\) and \(\vec{F}_N2\)**: These are the normal forces exerted by the ground on each wheel, acting vertically upwards. They counteract the weight of the box.
   - **\(\vec{F}_r1\) and \(\vec{F}_r2\)**: These are the frictional forces at each wheel, acting horizontally. They oppose the motion due to the force applied.
   - **\(\vec{F}_w\)**: This is the weight of the box, acting vertically downwards, denoted by the arrow pointing down from the center of the box.

3. **Applied Force**:
   - **\(\vec{F}\)**: This is the external force applied to the box, shown by a vector inclined at an angle \(\theta\) to the horizontal direction. The vector indicates the direction and magnitude of the applied force.
   - **Displacement**: Accompanied by a horizontal arrow, indicating the direction in which the box is expected to move.

The diagram is crucial for understanding how different forces interact to cause motion in the system, especially in scenarios involving friction and inclined forces.
Transcribed Image Text:The image illustrates the forces acting on a box that is placed on wheels and situated on a horizontal surface. Here's a detailed breakdown of the diagram: 1. **Box on Wheels**: The box is shown resting on two wheels, indicating that it can move along the surface. 2. **Forces Acting on the Box**: - **\(\vec{F}_N1\) and \(\vec{F}_N2\)**: These are the normal forces exerted by the ground on each wheel, acting vertically upwards. They counteract the weight of the box. - **\(\vec{F}_r1\) and \(\vec{F}_r2\)**: These are the frictional forces at each wheel, acting horizontally. They oppose the motion due to the force applied. - **\(\vec{F}_w\)**: This is the weight of the box, acting vertically downwards, denoted by the arrow pointing down from the center of the box. 3. **Applied Force**: - **\(\vec{F}\)**: This is the external force applied to the box, shown by a vector inclined at an angle \(\theta\) to the horizontal direction. The vector indicates the direction and magnitude of the applied force. - **Displacement**: Accompanied by a horizontal arrow, indicating the direction in which the box is expected to move. The diagram is crucial for understanding how different forces interact to cause motion in the system, especially in scenarios involving friction and inclined forces.
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