Question
A push broom is being pushed down across a rough floor. The broom moves to the right.
A picture of a person standing pushing a broom downward at an angle to the right. There is a velocity vector below the head of the broom pointing right, labeled v.
What is the correct free body diagram of the broom?
A free body diagram with 4 force vectors. The first vector is pointing downward, labeled F Subscript g Baseline. The second is pointing right, labeled F Subscript p Baseline. The third vector is pointing upward, labeled F Subscript N Baseline. The fourth vector is pointing left, labeled F Subscript f. The upward vector is the same length as the downward vector. The right vector is the same length as the left vector.
A free body diagram with 3 force vectors. The first vector is pointing downward, labeled F Subscript g Baseline. The second vector is pointing right, labeled F Subscript p Baseline. The third vector is pointing upward, labeled F Subscript N Baseline. All three vectors are of equal length.
A free body diagram with 4 force vectors. The first vector is pointing downward, labeled F Subscript g Baseline. The second vector is pointing right, labeled F Subscript f Baseline. The third vector is pointing upward, labeled F Subscript N Baseline. The fourth vector is pointing up to the left, labeled F Subscript P Baseline.
A free body diagram with 4 force vectors. The first vector is pointing downward, labeled F Subscript g Baseline. The second vector is pointing left, labeled F Subscript f Baseline. The third vector is pointing upward, labeled F Subscript N Baseline. The fourth vector is pointing down to the right, labeled F Subscript P Baseline. All vectors are the same length.
A picture of a person standing pushing a broom downward at an angle to the right. There is a velocity vector below the head of the broom pointing right, labeled v.
What is the correct free body diagram of the broom?
A free body diagram with 4 force vectors. The first vector is pointing downward, labeled F Subscript g Baseline. The second is pointing right, labeled F Subscript p Baseline. The third vector is pointing upward, labeled F Subscript N Baseline. The fourth vector is pointing left, labeled F Subscript f. The upward vector is the same length as the downward vector. The right vector is the same length as the left vector.
A free body diagram with 3 force vectors. The first vector is pointing downward, labeled F Subscript g Baseline. The second vector is pointing right, labeled F Subscript p Baseline. The third vector is pointing upward, labeled F Subscript N Baseline. All three vectors are of equal length.
A free body diagram with 4 force vectors. The first vector is pointing downward, labeled F Subscript g Baseline. The second vector is pointing right, labeled F Subscript f Baseline. The third vector is pointing upward, labeled F Subscript N Baseline. The fourth vector is pointing up to the left, labeled F Subscript P Baseline.
A free body diagram with 4 force vectors. The first vector is pointing downward, labeled F Subscript g Baseline. The second vector is pointing left, labeled F Subscript f Baseline. The third vector is pointing upward, labeled F Subscript N Baseline. The fourth vector is pointing down to the right, labeled F Subscript P Baseline. All vectors are the same length.
Answers
GPT-4o mini
In order to correctly analyze the forces acting on the broom in this scenario, let's consider each of the forces involved:
1. **Weight (F_g)** - This is the force due to gravity acting downward.
2. **Normal Force (F_N)** - This is the support force exerted by the floor acting upward.
3. **Friction (F_f)** - This is the force opposing the motion of the broom, which acts to the left since the broom is moving to the right.
4. **Push Force (F_P)** - This is the force applied by the person pushing the broom. Given that the broom is being pushed downward at an angle (downward and to the right), the push force has both a vertical and a horizontal component. However, for the free body diagram, the resulting force vector (combined effect of both components) will be angled down to the right.
Now, let's determine which option reflects these forces accurately:
- **Option 1:** This includes the downward force (F_g), the right force (F_p), the upward force (F_N), and the left force (F_f), with the upward and downward forces being equal in length, and the right vector being equal to the left vector. This seems plausible if we take into account that the push force is indeed directed at an angle.
- **Option 2:** This has three vectors and does not include friction (F_f), which is necessary since the broom is moving across a rough floor.
- **Option 3:** Here, the labels of the forces are misleading. F_f is moving to the right; it should go to the left to account for friction.
- **Option 4:** This shows friction opposing the motion to the left, the normal force acting upwards, the weight acting downwards, and the push force directed down to the right. The push force is not straight down; it's angled hence it should not be represented as vertically downward.
Based on this analysis, **Option 1** best describes the scenario since it accurately includes all forces acting on the broom and their relationships, where weight force is down, normal force is up, friction (F_f) acts to the left, and the push force (F_p) acts down to the right, ensuring that the lengths of opposing forces balance out.
1. **Weight (F_g)** - This is the force due to gravity acting downward.
2. **Normal Force (F_N)** - This is the support force exerted by the floor acting upward.
3. **Friction (F_f)** - This is the force opposing the motion of the broom, which acts to the left since the broom is moving to the right.
4. **Push Force (F_P)** - This is the force applied by the person pushing the broom. Given that the broom is being pushed downward at an angle (downward and to the right), the push force has both a vertical and a horizontal component. However, for the free body diagram, the resulting force vector (combined effect of both components) will be angled down to the right.
Now, let's determine which option reflects these forces accurately:
- **Option 1:** This includes the downward force (F_g), the right force (F_p), the upward force (F_N), and the left force (F_f), with the upward and downward forces being equal in length, and the right vector being equal to the left vector. This seems plausible if we take into account that the push force is indeed directed at an angle.
- **Option 2:** This has three vectors and does not include friction (F_f), which is necessary since the broom is moving across a rough floor.
- **Option 3:** Here, the labels of the forces are misleading. F_f is moving to the right; it should go to the left to account for friction.
- **Option 4:** This shows friction opposing the motion to the left, the normal force acting upwards, the weight acting downwards, and the push force directed down to the right. The push force is not straight down; it's angled hence it should not be represented as vertically downward.
Based on this analysis, **Option 1** best describes the scenario since it accurately includes all forces acting on the broom and their relationships, where weight force is down, normal force is up, friction (F_f) acts to the left, and the push force (F_p) acts down to the right, ensuring that the lengths of opposing forces balance out.