Table of contents

0. Math Review31m
- Math Review
  31m
1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
3. Vectors2h 43m
4. 2D Kinematics1h 42m
5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
7. Friction, Inclines, Systems2h 44m
8. Centripetal Forces & Gravitation7h 26m
9. Work & Energy1h 59m
10. Conservation of Energy2h 54m
11. Momentum & Impulse3h 40m
12. Rotational Kinematics2h 59m
13. Rotational Inertia & Energy7h 4m
14. Torque & Rotational Dynamics2h 5m
15. Rotational Equilibrium3h 39m
16. Angular Momentum3h 6m
17. Periodic Motion2h 9m
18. Waves & Sound3h 40m
19. Fluid Mechanics4h 27m
20. Heat and Temperature3h 7m
21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
23. The Second Law of Thermodynamics3h 11m
24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
29. Sources of Magnetic Field2h 30m
30. Induction and Inductance3h 38m
31. Alternating Current2h 37m
32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

6. Intro to Forces (Dynamics)

Forces in Connected Systems of Objects

Physics

6. Intro to Forces (Dynamics)

Forces in Connected Systems of Objects

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Multiple Choice

A 0.540-kg bucket rests on a scale. Into this bucket, you pour sand at the constant rate of 70.0 g/s. If the sand lands in the bucket with a speed of 4.50 m/s, what is the reading of the scale when there is 0.720 kg of sand in the bucket?

15.6 N

12.0 N

10.5 N

13.8 N

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Verified step by step guidance

First, identify the forces acting on the bucket. The scale measures the normal force, which is the sum of the gravitational force on the bucket and the sand, and the force due to the change in momentum of the sand as it lands in the bucket.

Calculate the gravitational force on the bucket and the sand. Use the formula: \( F_{gravity} = (m_{bucket} + m_{sand}) \times g \), where \( m_{bucket} = 0.540 \text{ kg} \), \( m_{sand} = 0.720 \text{ kg} \), and \( g = 9.81 \text{ m/s}^2 \).

Determine the rate of change of momentum of the sand as it lands in the bucket. The change in momentum per second (force) is given by \( F_{momentum} = \dot{m} \times v \), where \( \dot{m} = 0.070 \text{ kg/s} \) is the rate of sand flow and \( v = 4.50 \text{ m/s} \) is the speed of the sand.

Add the gravitational force and the force due to the change in momentum to find the total force (normal force) on the scale: \( F_{total} = F_{gravity} + F_{momentum} \).

The reading of the scale is equal to the total force calculated in the previous step. This is the force that the scale measures, which is the sum of the gravitational force and the force due to the change in momentum of the sand.