Ch 02: Motion Along a Straight Line

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo

Young & Freedman Calc 14th Edition

Ch 02: Motion Along a Straight Line

Problema 33

Capitolo 2, Problema 33

A small block has constant acceleration as it slides down a frictionless incline. The block is released from rest at the top of the incline, and its speed after it has traveled $6.80$ m to the bottom of the incline is $3.80$ m/s. What is the speed of the block when it is $3.40$ m from the top of the incline?

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Identify the known values: initial speed (u) = 0 m/s (since the block is released from rest), final speed (v) = 3.80 m/s after traveling a distance (s) = 6.80 m.

Use the kinematic equation for constant acceleration: $ v^2 = u^2 + 2as $ to find the acceleration (a). Substitute the known values: $ (3.80)^2 = 0 + 2a(6.80) $. Solve for a.

Once the acceleration is found, use it to determine the speed of the block when it is 3.40 m from the top. Use the same kinematic equation: $ v^2 = u^2 + 2as $, where s = 3.40 m.

Substitute the known values into the equation: $ v^2 = 0 + 2a(3.40) $.

Solve for the new speed (v) when the block has traveled 3.40 m down the incline.

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Kinematics

Kinematics is the branch of physics that deals with the motion of objects without considering the forces that cause the motion. It involves equations that relate displacement, velocity, acceleration, and time. In this problem, kinematic equations help determine the block's speed at different points along the incline.

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Kinematics Equations

Constant Acceleration

Constant acceleration implies that the rate of change of velocity is uniform over time. This simplifies calculations as the kinematic equations can be applied directly. For the block on the incline, knowing it has constant acceleration allows us to use these equations to find its speed at any point along the path.

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Energy Conservation

Energy conservation in physics states that the total energy in a closed system remains constant. For a frictionless incline, mechanical energy (potential and kinetic) is conserved. As the block slides down, potential energy converts to kinetic energy, allowing us to calculate its speed at different positions using energy principles.

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