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Ch 02: Motion Along a Straight Line
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 15th EditionCh 02: Motion Along a Straight LineProblem 34a
Chapter 2, Problem 34a

You throw a glob of putty straight up toward the ceiling, which is 3.603.60 m above the point where the putty leaves your hand. The initial speed of the putty as it leaves your hand is 9.509.50 m/s. What is the speed of the putty just before it strikes the ceiling?

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Identify the known values: the initial speed of the putty \( v_0 = 9.50 \text{ m/s} \), the distance to the ceiling \( d = 3.60 \text{ m} \), and the acceleration due to gravity \( g = 9.81 \text{ m/s}^2 \) (acting downward).
Use the kinematic equation for motion under constant acceleration to find the final speed \( v \) of the putty just before it strikes the ceiling: \( v^2 = v_0^2 + 2ad \), where \( a = -g \) because gravity is acting in the opposite direction to the motion.
Substitute the known values into the equation: \( v^2 = (9.50)^2 + 2(-9.81)(3.60) \).
Calculate the expression inside the square root to find \( v^2 \).
Take the square root of the result from the previous step to find the final speed \( v \) of the putty just before it strikes the ceiling.

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Key Concepts

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

Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration. They relate displacement, initial velocity, final velocity, acceleration, and time. In this problem, the equation v^2 = u^2 + 2as is useful, where v is the final velocity, u is the initial velocity, a is the acceleration (gravity, in this case), and s is the displacement.
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Gravitational Acceleration

Gravitational acceleration is the acceleration of an object due to Earth's gravity, approximately 9.81 m/s² downward. It affects the motion of the putty as it travels upward, slowing it down until it reaches its peak height, and then accelerating it downward as it approaches the ceiling.
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Conservation of Energy

The conservation of energy principle states that energy in a closed system remains constant. As the putty moves upward, its kinetic energy is converted into potential energy. Just before it hits the ceiling, the potential energy is converted back into kinetic energy, allowing us to calculate its speed using energy considerations.
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Related Practice
Textbook Question

You throw a glob of putty straight up toward the ceiling, which is 3.603.60 m above the point where the putty leaves your hand. The initial speed of the putty as it leaves your hand is 9.509.50 m/s. How much time from when it leaves your hand does it take the putty to reach the ceiling?

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Textbook Question

A tennis ball on Mars, where the acceleration due to gravity is 0.379g0.379g and air resistance is negligible, is hit directly upward and returns to the same level 8.58.5 s later. How high above its original point did the ball go?

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Textbook Question

A small rock is thrown vertically upward with a speed of 22.022.0 m/s from the edge of the roof of a 30.030.0-m-tall building. The rock doesn't hit the building on its way back down and lands on the street below. Ignore air resistance. What is the speed of the rock just before it hits the street?

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Textbook Question

A small rock is thrown vertically upward with a speed of 22.022.0 m/s from the edge of the roof of a 30.030.0-m-tall building. The rock doesn't hit the building on its way back down and lands on the street below. Ignore air resistance. How much time elapses from when the rock is thrown until it hits the street?

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Textbook Question

A juggler throws a bowling pin straight up with an initial speed of 8.208.20 m/s. How much time elapses until the bowling pin returns to the juggler's hand?

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Textbook Question

A tennis ball on Mars, where the acceleration due to gravity is 0.379g0.379g and air resistance is negligible, is hit directly upward and returns to the same level 8.58.5 s later. How fast was it moving just after it was hit?

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views