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A disk of radius $25.0 \mathrm{~cm}$ is free to turn about an axle perpendicular to it through its center. It has very thin but strong string wrapped around its rim, and the string is attached to a ball that is pulled tangentially away from the rim of the disk (Fig. $\mathbf{P 9 . 6 1}$ ). The pull increases in magnitude and produces an acceleration of the ball that obeys the equation $a(t)=A t,$ where $t$ is in seconds and $A$ is a constant. The cylinder starts from rest, and at the end of the third second, the ball's acceleration is $1.80 \mathrm{~m} / \mathrm{s}^{2}$. (a) Find $A$. (b) Express the angular acceleration of the disk as a function of time. (c) How much time after the disk has begun to turn does it reach an angular speed of $15.0 \mathrm{rad} / \mathrm{s} ?$ (d) Through what angle has the disk turned just as it reaches $15.0 \mathrm{rad} / \mathrm{s} ?$ (Hint: See Section $2.6 .)$

A disk of radius $25.0 \mathrm{~cm}$ is free to turn about an axle perpendicular to it through its center. It has very thin but strong string wrapped around its rim, and the string is attached to a ball that is pulled tangentially away from the rim of the disk (Fig. $\mathbf{P 9 . 6 1}$ ). The pull increases in magnitude and produces an acceleration of the ball that obeys the equation $a(t)=A t,$ where $t$ is in seconds and $A$ is a constant. The cylinder starts from rest, and at the end of the third second, the ball's acceleration is $1.80 \mathrm{~m} / \mathrm{s}^{2}$. (a) Find $A$. (b) Express the angular acceleration of the disk as a function of time. (c) How much time after the disk has begun to turn does it reach an angular speed of $15.0 \mathrm{rad} / \mathrm{s} ?$ (d) Through what angle has the disk turned just as it reaches $15.0 \mathrm{rad} / \mathrm{s} ?$ (Hint: See Section $2.6 .)$

University Physics with Modern Physics

A $15.0 \mathrm{~kg}$ fish swimming at $1.10 \mathrm{~m} / \mathrm{s}$ suddenly gobbles up a $4.50 \mathrm{~kg}$ fish that is initially stationary, Ignore any drag effects of the Water. (a) Find the speed of the large fish just after it eats the small one. (b) How much total mechanical energy was dissipated during this meal?

A $15.0 \mathrm{~kg}$ fish swimming at $1.10 \mathrm{~m} / \mathrm{s}$ suddenly gobbles up a $4.50 \mathrm{~kg}$ fish that is initially stationary, Ignore any drag effects of the Water. (a) Find the speed of the large fish just after it eats the small one. (b) How much total mechanical energy was dissipated during this meal?

University Physics with Modern Physics

A 2540-kg test rocket is launched vertically from the launch pad. Its fuel (of negligible mass) provides a thrust force such that its vertical velocity as a function of time is given by $v(t) = At + Bt^2$, where $A$ and $B$ are constants and time is measured from the instant the fuel is ignited. The rocket has an upward acceleration of 1.50 m/s$^2$ at the instant of ignition and, 1.00 s later, an upward velocity of 2.00 m>s. (a) Determine $A$ and $B$, including their SI units. (b) At 4.00 s after fuel ignition, what is the acceleration of the rocket, and (c) what thrust force does the burning fuel exert on it, assuming no air resistance? Express the thrust in newtons and as a multiple of the rocket's weight. (d) What was the initial thrust due to the fuel?

A 2540-kg test rocket is launched vertically from the launch pad. Its fuel (of negligible mass) provides a thrust force such that its vertical velocity as a function of time is given by $v(t) = At + Bt^2$, where $A$ and $B$ are constants and time is measured from the instant the fuel is ignited. The rocket has an upward acceleration of 1.50 m/s$^2$ at the instant of ignition and, 1.00 s later, an upward velocity of 2.00 m>s. (a) Determine $A$ and $B$, including their SI units. (b) At 4.00 s after fuel ignition, what is the acceleration of the rocket, and (c) what thrust force does the burning fuel exert on it, assuming no air resistance? Express the thrust in newtons and as a multiple of the rocket's weight. (d) What was the initial thrust due to the fuel?

University Physics with Modern Physics

Applying Newton's Laws

Using Newton's Second Law: Dynamics of…
An object with mass $m$ is moving along the $x$ -axis according to the equation $x(t)=\alpha t^{2}-2 \beta t,$ where $\alpha$ and $\beta$ are positive constants. What is the magnitude of the net force on the object at time $t=0 ?$

An object with mass $m$ is moving along the $x$ -axis according to the equation $x(t)=\alpha t^{2}-2 \beta t,$ where $\alpha$ and $\beta$ are positive constants. What is the magnitude of the net force on the object at time $t=0 ?$

University Physics with Modern Physics

Questions asked

ANSWERED

Samriddhi Singh verified

Numerade educator

What is the directional angle θ of vector B⃗ in the xy -plane measured counterclockwise from the +x -direction?

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ANSWERED

Prabhakar Kumar verified

Numerade educator

A 2540 kg test rocket is launched vertically from the launch pad. Its fuel (of negligible mass) provides a thrust force such that its vertical velocity as a function of time is given by v(t)=At+Bt2 , where A and B are constants and time is measured from the instant the fuel is ignited. The rocket has an upward acceleration of 1.60 m/s2 at the instant of ignition and, 1.00 s later, an upward velocity of 2.00 m/s Determine A . .

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Ivan Kochetkov verified

Numerade educator

A remote-controlled car is moving in a vacant parking lot. The velocity of the car as a function of time is given by vec{v} = [5.00 m/s - (0.0180 m/s^3)t^2] i + [2.00 m/s + (0.550 m/s^2)t] j. Part B What is a_y(t), the y-component of the acceleration of the car as function of time? a_y(t) = (-0.550 m/s^2)t a_y(t) = 2.00 m/s + (0.550 m/s^2)t a_y(t) = 2.00 m/s^2 a_y(t) = 0.550 m/s^2 Part C What is the magnitude of the velocity of the car at t = 7.50 s? Express your answer with the appropriate units. v = Part D What is the direction (in degrees counterclockwise from +x-axis) of the velocity of the car at t = 7.50 s? Express your answer in degrees. heta_v = 116.15 Part E What is the magnitude of the acceleration of the car at t = 7.50 s? Express your answer with the appropriate units. a =

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