A hockey puck with mass 0.1600.160 kg is at rest at the origin (x=0x = 0) on the horizontal, frictionless surface of the rink. At time t=0t = 0 a player applies a force of 0.2500.250 N to the puck, parallel to the xx-axis; she continues to apply this force until t=2.00t = 2.00 s. What are the position and speed of the puck at t=2.00t = 2.00 s?

Ch 04: Newton's Laws of Motion

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th Edition

Ch 04: Newton's Laws of Motion

Problema 11a

Capitolo 4, Problema 11a

A hockey puck with mass $0.160$ kg is at rest at the origin ( $x equals 0$ ) on the horizontal, frictionless surface of the rink. At time $t equals 0$ a player applies a force of $0.250$ N to the puck, parallel to the $x$ -axis; she continues to apply this force until $t equals 2.00$ s. What are the position and speed of the puck at $t equals 2.00$ s?

Guida verificata passo dopo passo

Step 1: Identify the given values and relevant equations. The mass of the puck is 0.160 kg, the applied force is 0.250 N, and the time duration is 2.00 s. Since the surface is frictionless, Newton's second law applies:

F = m a

, where

a

is the acceleration.

Step 2: Calculate the acceleration of the puck using Newton's second law. Rearrange the equation to solve for acceleration:

a = \frac{F}{m}

. Substitute the values of

F

and

m

Step 3: Use the kinematic equation to find the velocity of the puck at

t = 2.00

s. The equation is

v = v_i + a t

, where

v_i

is the initial velocity (0 m/s, since the puck starts at rest). Substitute the values of

a

and

t

Step 4: Use the kinematic equation to find the position of the puck at

t = 2.00

s. The equation is

x = x_i + v_i t + \frac{1}{2} a t^2

, where

x_i

is the initial position (0 m). Substitute the values of

v_i

a

, and

t

Step 5: Combine the results from Steps 3 and 4 to summarize the position and velocity of the puck at

t = 2.00

s. Ensure all units are consistent and verify the calculations conceptually.

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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. In this scenario, the applied force on the hockey puck will determine its acceleration, which is crucial for calculating its position and speed over time.

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Percorso guidato

06:54

Intro to Forces & Newton's Second Law

Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration. They relate displacement, initial velocity, final velocity, acceleration, and time. For this problem, the relevant equations will help determine the puck's position and speed after 2 seconds, given its initial state of rest and the constant force applied.

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Percorso guidato

08:25

Kinematics Equations

Uniform Acceleration

Uniform acceleration occurs when an object's velocity changes at a constant rate. In this case, the hockey puck experiences uniform acceleration due to the constant force applied by the player. Understanding this concept is essential for predicting how the puck's speed and position evolve over the 2-second interval, as it simplifies the calculations using the kinematic equations.

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05:47

Intro to Acceleration

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