Three sleds are being pulled horizontally on frictionless horizontal ice using horizontal ropes (Fig. E5.145.145.14). The pull is of magnitude 190190190 N. Find the acceleration of the system.

Ch 05: Applying Newton's Laws

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

All textbooks

Young & Freedman Calc 14th Edition

Ch 05: Applying Newton's Laws

Problem 14a

Chapter 5, Problem 14a

Three sleds are being pulled horizontally on frictionless horizontal ice using horizontal ropes (Fig. E $5.14$ ). The pull is of magnitude $190$ N. Find the acceleration of the system.

Verified step by step guidance

Step 1: Identify the total mass of the system. The sleds have masses of 30.0 kg, 20.0 kg, and 10.0 kg. Add these together to find the total mass: $ m_{\text{total}} = 30.0 \, \text{kg} + 20.0 \, \text{kg} + 10.0 \, \text{kg} $.

Step 2: Recall Newton's Second Law of Motion, $ F = m \cdot a $, where $ F $ is the net force, $ m $ is the total mass, and $ a $ is the acceleration. Rearrange the formula to solve for acceleration: $ a = \frac{F}{m} $.

Step 3: Substitute the given values into the formula. The pulling force is $ F = 190 \, \text{N} $, and the total mass $ m_{\text{total}} $ was calculated in Step 1.

Step 4: Perform the division $ a = \frac{190 \, \text{N}}{m_{\text{total}}} $ to find the acceleration of the system. Ensure the units are consistent (N for force and kg for mass).

Step 5: Interpret the result. The acceleration $ a $ represents the rate at which the sleds are speeding up on the frictionless ice under the applied force.

Verified video answer for a similar problem:

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

Video duration:

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 relationship is expressed by the formula F = ma, where F is the net force, m is the mass, and a is the acceleration. In this scenario, the total mass of the sleds and the applied force will determine the system's acceleration.

Net Force

The net force is the vector sum of all the forces acting on an object. In the context of the sleds, the net force is the pulling force applied to the system minus any opposing forces, which in this case is negligible due to the frictionless surface. Understanding net force is crucial for calculating the resulting acceleration of the entire system of sleds.

Mass and Acceleration Relationship

The relationship between mass and acceleration is fundamental in physics. A larger mass will result in a smaller acceleration for the same applied force, as indicated by Newton's Second Law. In this problem, the combined mass of the sleds (30 kg + 20 kg + 10 kg) will affect how quickly the system accelerates when the 190 N force is applied.

Recommended video:

Guided course

03:42

Torque & Acceleration of a Point Mass

Related Practice

Textbook Question

An $8.00$ -kg block of ice, released from rest at the top of a $1.50$ -m-long frictionless ramp, slides downhill, reaching a speed of $2.50$ m/s at the bottom. What is the angle between the ramp and the horizontal?

3813

views

Textbook Question

An $8.00$ -kg block of ice, released from rest at the top of a $1.50$ -m-long frictionless ramp, slides downhill, reaching a speed of $2.50$ m/s at the bottom. What would be the speed of the ice at the bottom if the motion were opposed by a constant friction force of $10.0$ N parallel to the surface of the ramp?

1477

views

Textbook Question

On September 8, 2004, the Genesis spacecraft crashed in the Utah desert because its parachute did not open. The $210$ -kg capsule hit the ground at $311$ km/h and penetrated the soil to a depth of $81.0$ cm. What was its acceleration (in m/s² and in g's), assumed to be constant, during the crash?

1585

views

Textbook Question

On September 8, 2004, the Genesis spacecraft crashed in the Utah desert because its parachute did not open. The $210$ -kg capsule hit the ground at $311$ km/h and penetrated the soil to a depth of $81.0$ cm. What force did the ground exert on the capsule during the crash? Express the force in newtons and as a multiple of the capsule's weight.

2675

views

Textbook Question

Three sleds are being pulled horizontally on frictionless horizontal ice using horizontal ropes (Fig. E $5.14$ ). The pull is of magnitude $190$ N. Find the tension in ropes $A$ and $B$ .

An astronaut is inside a $2.25 × 10^6$ kg rocket that is blasting off vertically from the launch pad. You want this rocket to reach the speed of sound ( $331$ m/s) as quickly as possible, but astronauts are in danger of blacking out at an acceleration greater than $4g$ . What force, in terms of the astronaut's weight $w$ , does the rocket exert on her? Start with a free-body diagram of the astronaut.

2944

views

rank