A 45.045.045.0-kg crate of tools rests on a horizontal floor. You exert a gradually increasing horizontal push on it, and the crate just begins to move when your force exceeds 313313313 N. Then you must reduce your push to 208208208 N to keep it moving at a steady 25.025.025.0 cm/s. What push must you exert to give it an acceleration of 1.101.10 m/s2?

Ch 05: Applying Newton's Laws

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook

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Young & Freedman Calc 15th Edition

Ch 05: Applying Newton's Laws

Problem 27b

Chapter 5, Problem 27b

A $45.0$ -kg crate of tools rests on a horizontal floor. You exert a gradually increasing horizontal push on it, and the crate just begins to move when your force exceeds $313$ N. Then you must reduce your push to $208$ N to keep it moving at a steady $25.0$ cm/s. What push must you exert to give it an acceleration of $1.10$ m/s²?

Verified step by step guidance

Step 1: Identify the forces acting on the crate. The forces include the applied force (F), the force of kinetic friction (F_k), and the net force (F_net). The force of kinetic friction is given as 208 N when the crate is moving at a constant velocity.

Step 2: Use Newton's second law of motion, which states that F_net = m * a, where m is the mass of the crate (45.0 kg) and a is the acceleration (1.10 m/s²). The net force is the difference between the applied force (F) and the force of kinetic friction (F_k).

Step 3: Write the equation for the net force: F_net = F - F_k. Substitute F_net = m * a into this equation to get F - F_k = m * a.

Step 4: Rearrange the equation to solve for the applied force (F): F = F_k + m * a. Substitute the known values: F_k = 208 N, m = 45.0 kg, and a = 1.10 m/s².

Step 5: Perform the calculation to find the applied force (F). This will give you the force required to accelerate the crate at 1.10 m/s² while overcoming the force of kinetic friction.

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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. Understanding this law is crucial for determining the force required to accelerate the crate.

Friction

Friction is the force that opposes the relative motion of two surfaces in contact. In this scenario, static friction prevents the crate from moving until a certain threshold force is applied, while kinetic friction acts on the crate once it is in motion. The coefficients of static and kinetic friction are essential for calculating the forces involved in moving the crate.

Net Force

The net force is the vector sum of all the forces acting on an object. In the context of the crate, the net force is the difference between the applied force and the frictional force opposing the motion. To achieve a specific acceleration, the applied force must overcome both static and kinetic friction, resulting in the necessary net force to produce the desired acceleration.

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Related Practice

Textbook Question

A pickup truck is carrying a toolbox, but the rear gate of the truck is missing. The toolbox will slide out if it is set moving. The coefficients of kinetic friction and static friction between the box and the level bed of the truck are $0.355$ and $0.650$ , respectively. Starting from rest, what is the shortest time this truck could accelerate uniformly to $30.0$ m/s without causing the box to slide? Draw a free-body diagram of the toolbox.

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Textbook Question

A box of bananas weighing $40.0$ N rests on a horizontal surface. The coefficient of static friction between the box and the surface is $0.40$ , and the coefficient of kinetic friction is $0.20$ . What minimum horizontal force must the monkey apply to keep the box moving at constant velocity once it has been started?

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Textbook Question

A box of bananas weighing $40.0$ N rests on a horizontal surface. The coefficient of static friction between the box and the surface is $0.40$ , and the coefficient of kinetic friction is $0.20$ . If the monkey applies a horizontal force of $18.0$ N, what is the magnitude of the friction force and what is the box's acceleration?

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Textbook Question

A $45.0$ -kg crate of tools rests on a horizontal floor. You exert a gradually increasing horizontal push on it, and the crate just begins to move when your force exceeds $313$ N. Then you must reduce your push to $208$ N to keep it moving at a steady $25.0$ cm/s. Suppose you were performing the same experiment on the moon, where the acceleration due to gravity is $1.62$ m/s².

(i) What magnitude push would cause it to move?

(ii) What would its acceleration be if you maintained the push in part (b)? Note: Part (b) asked what push you must exert to give it an acceleration of $1.10$ m/s².

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Textbook Question

A $25.0$ -kg box of textbooks rests on a loading ramp that makes an angle $α$ with the horizontal. The coefficient of kinetic friction is $0.25$ , and the coefficient of static friction is $0.35$ . At this angle, find the acceleration once the box has begun to move.

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Textbook Question

A $45.0$ -kg crate of tools rests on a horizontal floor. You exert a gradually increasing horizontal push on it, and the crate just begins to move when your force exceeds $313$ N. Then you must reduce your push to $208$ N to keep it moving at a steady $25.0$ cm/s. What are the coefficients of static and kinetic friction between the crate and the floor?

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