The Following Questions Ask You To Solve Problems Involving

The Following Questions Ask You To Solve Problems Involving Newtons L

The following questions ask you to solve problems involving Newton's laws and forces. Work out each problem on paper, and post a scanned image of your work for each question, along with a brief description of how you solved the problem. Your scanned work should include a free body diagram showing all forces acting on the object(s), as well as a step-by-step solution to the problem and upload your responses to the same W2 Assignment 2 Dropbox.

Question 1: A 2 kg book resting on a flat table requires an applied force of 4 N to make it move. Draw a free body diagram illustrating this situation and find the coefficient of static friction between the book and the table.

Question 2: A 30 kg crate is pulled across a flat floor with 80 N of force. The coefficient of kinetic friction between the crate and the floor is 0.15. Draw a free body diagram illustrating this situation and find the acceleration of the crate.

Question 3: An applied force of 100 N causes a 20 kg crate to accelerate across a level floor at 2 m/s². Draw a free body diagram illustrating this situation and find the coefficient of kinetic friction between the crate and the floor.

Question 4: 60 N of force is applied to a 10 kg crate initially at rest on a level floor. The coefficient of friction between the crate and the floor is 0.4. Draw a free body diagram illustrating this situation and find the distance traveled and the velocity of the crate after 3 seconds.

Question 5: Sue and Bill are standing on a frictionless surface of ice. Sue, whose mass is 60 kg, pushes Bill, mass 100 kg, with 300 N of force. Draw a free body diagram illustrating this situation and find the acceleration of both Sue and Bill.

Paper For Above instruction

In this paper, we analyze five physics problems involving Newton's laws of motion, friction, and force interactions. Each problem requires drawing a free body diagram, applying Newton's second law, and solving for unknown variables such as the coefficient of friction, acceleration, or distance traveled. The following solutions comprehensively address each problem step-by-step.

Problem 1: Coefficient of Static Friction for a Moving Book

Given data: mass of the book (m) = 2 kg, applied force (F_app) = 4 N.

Since the book just starts to move, the applied force equals the maximum static friction (F_s_max).

The weight (W) of the book: W = m g = 2 kg 9.8 m/s² = 19.6 N.

The normal force (N): N = W = 19.6 N, assuming the table is horizontal.

The maximum static friction force: F_s_max = μ_s * N, where μ_s is the coefficient of static friction.

Because F_app = F_s_max at the threshold of motion:

4 N = μ_s * 19.6 N => μ_s = 4 / 19.6 ≈ 0.204.

Free Body Diagram: The forces on the book include gravity downward, normal force upward, and static friction and applied force acting horizontally.

The coefficient of static friction: μ_s ≈ 0.204.

Problem 2: Acceleration of a Pulled Crate

Given data: mass of crate (m) = 30 kg, applied force (F_applied) = 80 N, coefficient of kinetic friction (μ_k) = 0.15.

The normal force N = m g = 30 kg 9.8 m/s² = 294 N.

The kinetic friction force: F_friction = μ_k N = 0.15 294 = 44.1 N.

The net force causing acceleration: F_net = F_applied - F_friction = 80 N - 44.1 N = 35.9 N.

Using Newton's second law: a = F_net / m = 35.9 N / 30 kg ≈ 1.20 m/s².

Free Body Diagram: The applied force in one direction, kinetic friction opposing it, normal force upward, gravity downward.

Acceleration of the crate: approximately 1.20 m/s².

Problem 3: Friction Coefficient from Known Force and Acceleration

Given data: applied force (F) = 100 N, mass (m) = 20 kg, acceleration (a) = 2 m/s².

Calculate the normal force: N = m g = 20 kg 9.8 m/s² = 196 N.

According to Newton's second law: F_net = m a, so F_net = 20 kg 2 m/s² = 40 N.

The net force includes the applied force minus the kinetic friction: F - F_friction = F_net, so:

100 N - F_friction = 40 N => F_friction = 60 N.

Recall that F_friction = μ_k * N, so: μ_k = F_friction / N = 60 / 196 ≈ 0.306.

Free Body Diagram: Applied force forward, kinetic friction backward, gravity downward, normal force upward.

Friction coefficient μ_k ≈ 0.306.

Problem 4: Motion of a Crate Under Applied Force and Friction

Given data: applied force (F) = 60 N, mass (m) = 10 kg, coefficient of friction (μ) = 0.4, time (t) = 3 s.

Normal force: N = m g = 10 kg 9.8 m/s² = 98 N.

Friction force: F_friction = μ N = 0.4 98 = 39.2 N.

Net force: F_net = F - F_friction = 60 N - 39.2 N = 20.8 N.

Acceleration: a = F_net / m = 20.8 N / 10 kg = 2.08 m/s².

Initial velocity (u) = 0 (initial rest).

Velocity after 3 seconds: v = u + a t = 0 + 2.08 3 ≈ 6.24 m/s.

Distance traveled: s = u t + 0.5 a t² = 0 + 0.5 2.08 * 9 ≈ 9.36 meters.

Free Body Diagram: Force to the right, friction to the left, normal force upwards, gravity downward.

Final velocity after 3 seconds: approximately 6.24 m/s.

Problem 5: Push on a Frictionless Ice Surface

Given data: mass of Sue (m₁) = 60 kg, mass of Bill (m₂) = 100 kg, force applied (F) = 300 N.

The surface is frictionless, so only internal forces act between Sue and Bill.

Applying Newton's second law: F = m * a.

Since the force is applied by Sue on Bill, Bill's acceleration:

a₂ = F / m₂ = 300 N / 100 kg = 3 m/s².

Recoil of Sue: by Newton's third law, she experiences an equal and opposite force, so:

a₁ = F' / m₁, where F' is the force exerted by Bill on Sue.

But F' = F due to action-reaction pairs; thus, from conservation of momentum: m₁ a₁ = m₂ a₂.

Rearranged: a₁ = (m₂ / m₁) a₂ = (100 / 60) 3 ≈ 5 m/s².

Free Body Diagram: Both on frictionless surface, with equal and opposite forces between them, and external push applied to Bill.

Accelerations: Bill's acceleration is 3 m/s² forward; Sue's recoil acceleration is approximately 5 m/s² backward.

Conclusion

These problems demonstrate applying Newton's second law, analyzing forces in various situations, and calculating coefficients of friction, acceleration, and motion parameters. Drawing clear free body diagrams and setting equations accordingly are essential steps for solving such physics problems accurately.

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