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

Problem 11a

Chapter 4, Problem 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?

Verified step by step guidance

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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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. 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.

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.

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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Related Practice

Textbook Question

A hockey puck with mass $0.160$ kg is at rest at the origin ( $x = 0$ ) on the horizontal, frictionless surface of the rink. At time $t = 0$ a player applies a force of $0.250$ N to the puck, parallel to the $x$ -axis; she continues to apply this force until $t = 2.00$ s. If the same force is again applied at $t equals 5.00$ s, what are the position and speed of the puck at $t equals 7.00$ s?

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Textbook Question

A box rests on a frozen pond, which serves as a frictionless horizontal surface. If a fisherman applies a horizontal force with magnitude $48.0$ N to the box and produces an acceleration of magnitude $2.20$ m/s², what is the mass of the box?

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Textbook Question

A $4.50$ -kg experimental cart undergoes an acceleration in a straight line (the $x$ -axis). The graph in Fig. E $4.13$ shows this acceleration as a function of time. During what times is the net force on the cart a constant?

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Textbook Question

A dockworker applies a constant horizontal force of $80.0$ N to a block of ice on a smooth horizontal floor. The frictional force is negligible. The block starts from rest and moves $11.0$ m in $5.00$ s. What is the mass of the block of ice?

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Textbook Question

A $4.50$ -kg experimental cart undergoes an acceleration in a straight line (the $x$ -axis). The graph in Fig. E $4.13$ shows this acceleration as a function of time. Find the maximum net force on this cart. When does this maximum force occur?

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Textbook Question

You walk into an elevator, step onto a scale, and push the 'up' button. You recall that your normal weight is $625$ N. Draw a free-body diagram. If you hold a $3.85$ -kg package by a light vertical string, what will be the tension in this string when the elevator accelerates as in part (a)? Note: Part (a) asked what does the scale read when the elevator has an upward acceleration of magnitude $2.50$ m/s².

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