When jumping straight up from a crouched position, an average person can reach a maximum height of about 606060 cm. During the jump, the person's body from the knees up typically rises a distance of around 505050 cm. To keep the calculations simple and yet get a reasonable result, assume that the entire body rises this much during the jump. Draw a free-body diagram of the person during the jump.

Ch 05: Applying Newton's Laws

Young & Freedman Calc - University Physics 15th Edition

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Young & Freedman Calc 15th Edition

Ch 05: Applying Newton's Laws

Problem 19b

Chapter 5, Problem 19b

When jumping straight up from a crouched position, an average person can reach a maximum height of about $60$ cm. During the jump, the person's body from the knees up typically rises a distance of around $50$ cm. To keep the calculations simple and yet get a reasonable result, assume that the entire body rises this much during the jump. Draw a free-body diagram of the person during the jump.

Verified step by step guidance

Step 1: Understand the problem. The question asks for a free-body diagram of a person during the jump. A free-body diagram is a visual representation of all the forces acting on an object. In this case, the object is the person during the jump.

Step 2: Identify the forces acting on the person. During the jump, there are two primary forces to consider: (1) the gravitational force (weight) acting downward, which is equal to the person's mass multiplied by the acceleration due to gravity $ F_g = m \cdot g $, and (2) the upward normal force exerted by the ground, which is greater than the gravitational force during the jump to provide the upward acceleration.

Step 3: Represent the forces on the diagram. Draw a vertical arrow pointing downward to represent the gravitational force $ F_g $. Label this arrow as $ F_g = m \cdot g $. Then, draw a longer vertical arrow pointing upward to represent the normal force $ F_N $, which is greater than $ F_g $ during the jump. Label this arrow as $ F_N $.

Step 4: Indicate the net force direction. Since the person is accelerating upward during the jump, the net force $ F_{\text{net}} $ is directed upward. This net force is the result of the upward normal force being greater than the downward gravitational force, i.e., $ F_{\text{net}} = F_N - F_g $.

Step 5: Finalize the diagram. Ensure the diagram clearly shows the two forces ($ F_g $ and $ F_N $) with their respective directions and labels. The upward arrow ($ F_N $) should be longer than the downward arrow ($ F_g $) to reflect the net upward force during the jump.

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Key Concepts

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

Free-Body Diagram

A free-body diagram is a graphical representation used to visualize the forces acting on an object. In the context of a person jumping, it illustrates all the forces, such as gravity and the force exerted by the legs, acting on the body at a specific moment. This helps in analyzing the motion and understanding how these forces interact to influence the jump.

Forces in Motion

Forces in motion refer to the various forces that affect an object's movement. In a jump, the primary forces include gravitational force pulling the person down and the upward force generated by the legs during the jump. Understanding these forces is crucial for analyzing the dynamics of the jump and predicting the maximum height achieved.

Kinematics

Kinematics is the branch of physics that deals with the motion of objects without considering the forces that cause the motion. It involves concepts such as displacement, velocity, and acceleration. In the context of the jump, kinematics helps describe how the person's height changes over time and the relationship between the initial velocity and the maximum height reached.

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Textbook Question

When jumping straight up from a crouched position, an average person can reach a maximum height of about $60$ cm. During the jump, the person's body from the knees up typically rises a distance of around $50$ cm. To keep the calculations simple and yet get a reasonable result, assume that the entire body rises this much during the jump. In terms of this jumper's weight w, what force does the ground exert on him or her during the jump?

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Textbook Question

A $5.00$ -kg crate is suspended from the end of a short vertical rope of negligible mass. An upward force $F (t)$ is applied to the end of the rope, and the height of the crate above its initial position is given by $y (t) =$ ( $2.80$ m/s)t + ( $0.610$ m/s³)t³. What is the magnitude of $F$ when $t equals 4.00$ s?

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Textbook Question

A light rope is attached to a block with mass $4.00$ kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass m is suspended from the other end. When the blocks are released, the tension in the rope is $15.0$ N. Find $m$ .

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Textbook Question

When jumping straight up from a crouched position, an average person can reach a maximum height of about $60$ cm. During the jump, the person's body from the knees up typically rises a distance of around $50$ cm. To keep the calculations simple and yet get a reasonable result, assume that the entire body rises this much during the jump. With what initial speed does the person leave the ground to reach a height of $60$ cm?

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Textbook Question

A $2.00$ -kg box is moving to the right with speed $9.00$ m/s on a horizontal, frictionless surface. At $t equals 0$ a horizontal force is applied to the box. The force is directed to the left and has magnitude $F (t) =$ ( $6.00$ N/s²)t². What distance does the box move from its position at $t equals 0$ before its speed is reduced to zero?

Textbook Question

A light rope is attached to a block with mass $4.00$ kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass $m$ is suspended from the other end. When the blocks are released, the tension in the rope is $15.0$ N. How does the tension compare to the weight of the hanging block?

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