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There are separate answers for each part of this situation: 1. As the mover lifts the piece of furniture to the dolly, s/he will probably use a normal force (no friction) against the bottom of the piece, while at the same time pressing and lifting against the side of the piece, which would require static friction. 2. As the mover pushes the piece of furniture on the dolly across the floor, s/he would probably use only a normal force against the side of the piece (no friction), but there might be some static friction force involved if s/he is pushing at an angle against the piece. 3. As the piece of furniture moves with the dolly under it, it is pressing down on the dolly with a normal force and using static friction to bring the dolly along in the same direction the piece is moving. 4. As the dolly frame presses down on the axle of each wheel, it exerts a normal force on the bearing of the axle. There is probably no friction force involved. 5. As the axle turns within the bearing, there is a combination of static and kinetic friction as the ball bearings turn and slip inside the bearing. 6. As the wheel presses down on the floor, the floor presses up on the wheel with the same amount of normal force. The static friction force from the floor pulls back on the surface of the wheel at the point of contact and causes the wheel to turn.

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Q: When a mover puts furniture on a dolly with wheels which type of friction is the mover using?
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