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)

Newton's Third Law & Action-Reaction Pairs

Physics

6. Intro to Forces (Dynamics)

Newton's Third Law & Action-Reaction Pairs

Previous problemNext problem

6:40 minutes

Problem 8a

Textbook Question

A 1000 kg car is pushing an out-of-gear 2000 kg truck that has a dead battery. When the driver steps on the accelerator, the drive wheels of the car push horizontally against the ground with a force of 4500 N. Rolling friction can be neglected. What is the magnitude of the force of the car on the truck?

Verified step by step guidance

Step 1: Start by identifying the total system mass. The car has a mass of 1000 kg, and the truck has a mass of 2000 kg. Therefore, the total mass of the system is the sum of the two: \( m_{\text{total}} = 1000 \; \text{kg} + 2000 \; \text{kg} = 3000 \; \text{kg} \).

Step 2: Use Newton's Second Law of Motion, \( F = ma \), to calculate the acceleration of the system. The net force acting on the system is the force exerted by the car's drive wheels, \( F = 4500 \; \text{N} \). The acceleration of the system is given by \( a = \frac{F}{m_{\text{total}}} \). Substitute the values: \( a = \frac{4500}{3000} \; \text{m/s}^2 \).

Step 3: Focus on the interaction between the car and the truck. The force of the car on the truck is the same as the force required to accelerate the truck alone. Use Newton's Second Law again, \( F_{\text{car on truck}} = m_{\text{truck}} \cdot a \), where \( m_{\text{truck}} = 2000 \; \text{kg} \) and \( a \) is the acceleration calculated in Step 2.

Step 4: Substitute the values into the equation from Step 3: \( F_{\text{car on truck}} = 2000 \cdot a \). Use the acceleration value from Step 2 to complete the calculation.

Step 5: Conclude that the magnitude of the force of the car on the truck is equal to the force required to accelerate the truck at the same rate as the system. This force is determined by the truck's mass and the system's acceleration.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Newton's Second Law of Motion

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This law can be expressed with the formula F = ma, where F is the net force, m is the mass, and a is the acceleration. In this scenario, understanding how the forces interact between the car and the truck is crucial for determining the force exerted by the car on the truck.

Force Interaction

According to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. This means that when the car exerts a force on the truck, the truck exerts an equal force back on the car. This concept is essential for analyzing the forces at play in the system, particularly in understanding how the car's force affects the truck's motion.

System of Objects

In this problem, the car and truck can be considered as a single system. The total mass of the system affects how the forces are distributed and how the system accelerates. By treating the car and truck together, we can apply Newton's laws to find the force exerted by the car on the truck, taking into account the combined mass and the force applied by the car.

Watch next

Master Newton's Third Law & Action-Reaction Pairs with a bite sized video explanation from Patrick

Start learning

Related Videos

Related Practice

Textbook Question

A house painter uses the chair-and-pulley arrangement of FIGURE P7.45 to lift himself up the side of a house. The painter's mass is 70 kg and the chair's mass is 10 kg. With what force must he pull down on the rope in order to accelerate upward at 0.20 m/s².

A 75 kg archer on ice skates is standing at rest on very smooth ice. He shoots a 450 g arrow horizontally. When released, the arrow reaches a speed of 110 m/s in 0.25 s. Assume that the force of the bow string on the arrow is constant. What is the archer's recoil speed?

769

views

Textbook Question

The foot of a 55 kg sprinter is on the ground for 0.25 s while her body accelerates from rest to 2.0 m/s. What is the magnitude of the friction force?

1044

views

Textbook Question

Blocks with masses of 1 kg, 2 kg, and 3 kg are lined up in a row on a frictionless table. All three are pushed forward by a 12 N force applied to the 1 kg block. How much force does the 2 kg block exert on the 1 kg block?

2383

views

Textbook Question

How much force does the astronaut exert on his chair while accelerating straight up at 10 m/s²?

793

views

Multiple Choice

The Earth exerts a gravitational force of 50 N downward on a chair. What is the reaction force, and what is its value?

306

views

Multiple Choice

Which of the options is NOT an action-reaction pair in the following situation? A book slides across the floor, slowing down due to friction.