Dinámica - Ejercicios Resueltos - Nivel 2A

Summary

In this video, Jorge from Matemóvil explains a dynamic physics problem where a car is towing a 5-ton tank with a 9000 N tension force. The tank, initially at rest, reaches a speed of 3 m/s after 10 seconds. The goal is to calculate the frictional force between the tank and the ground. By applying Newton's second law and using the formula for motion, Jorge calculates the acceleration, and then the frictional force turns out to be 7500 N. This video demonstrates the steps to solve the problem, using clear diagrams and calculations to explain the physics concepts involved.

Takeaways

• 😀 A car of 1 ton is towing a 5-ton tank using a rope with a tension force of 9000 N.
• 😀 The tank starts from rest (0 m/s) and after 10 seconds reaches a velocity of 3 m/s.
• 😀 The goal of the problem is to calculate the friction force between the tank and the ground.
• 😀 To solve the problem, we first need to calculate the acceleration of the tank using the kinematic equation: v_f = v_i + at.
• 😀 The acceleration is calculated as 0.3 m/s² after applying the kinematic formula with the given data.
• 😀 Next, Newton's Second Law is applied to relate the forces acting on the tank in the direction of motion (x-axis).
• 😀 The forces acting on the tank are tension (9000 N) and the frictional force, which opposes the movement.
• 😀 The equation used is: Sum of Forces = mass × acceleration, leading to 9000 N - Friction Force = 5000 kg × 0.3 m/s².
• 😀 After solving for the frictional force, we find that the friction force is 7500 N.
• 😀 The friction force is acting opposite to the motion, preventing the tank from accelerating faster.
• 😀 The script concludes with encouragement to continue learning and invites viewers to subscribe to the channel.

Q & A

What is the main problem being solved in the video?

The main problem is calculating the frictional force between a tank and the ground while being towed by a car. The problem involves determining the frictional force based on the tension in the towing rope and the acceleration of the tank.

What are the key data points provided in the problem?

The key data points include: the mass of the car (1 ton), the mass of the tank (5 tons), the tension in the towing rope (9000 N), the initial state of the tank (at rest), the final velocity of the tank after 10 seconds (3 m/s), and the time taken for the tank to reach the final velocity (10 seconds).

How do you calculate acceleration in this scenario?

Acceleration is calculated using the kinematic equation: final velocity = initial velocity + acceleration × time. With an initial velocity of 0 m/s, a final velocity of 3 m/s, and a time of 10 seconds, the acceleration comes out to be 0.3 m/s².

What is the formula used to calculate the frictional force?

The frictional force is calculated using Newton’s second law in the x-direction: sum of forces = mass × acceleration. The forces considered are the tension in the rope (9000 N) and the frictional force opposing the movement. The frictional force is then found to be 7500 N.

Why is the frictional force acting opposite to the direction of movement?

The frictional force opposes the movement because friction always acts in the direction opposite to the motion of an object, resisting its motion along a surface.

How is the total mass involved in the system calculated?

The total mass in the system refers to the mass of the tank, which is 5 tons. In kilograms, this is 5000 kg, as 1 ton equals 1000 kg.

Why do we focus on the forces in the x-direction?

We focus on the x-direction because the problem specifically involves the horizontal motion of the tank, which is where the acceleration occurs. The forces in the x-direction include the tension and the frictional force.

What units are used for the final answer, and why?

The final answer for the frictional force is given in Newtons (N) because we are working in the International System of Units (SI), where force is measured in Newtons.

What is the significance of the tank being initially at rest?

The tank being initially at rest means its initial velocity is zero, which is an important condition for calculating acceleration. This allows the use of kinematic equations to determine the acceleration during the towing process.

What is the importance of drawing a free body diagram in this problem?

A free body diagram is crucial in visualizing and analyzing the forces acting on the tank. It helps in understanding how the tension in the rope, the frictional force, and the weight of the tank interact, and it is essential for applying Newton's second law to solve the problem.