Numerade

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Ely Crowder

Numerade educator

A firework is launched from ground level with speed 65m/s, at 22.62 degrees away from vertical and in the northern direction. At the instant that the firework reaches it's maximum height it explodes into four fragments which fly apart in a horizontal plane. The pieces are labelled N, S, W, E, and their masses and initial velocities as such: Masses: N: 4, W:3, S:1, E:2. Velocities: N: 2[north] W: -4[east] S: -8[north] E: 6[east] (a) Confirm that momentum is conserved just after the instant of the explosion(do this in the frame which is moving with the firework (b)(i) Compute the velocity of each particle, with respect to observers on the ground, just after the instant of the explosion (ii) Compute the total momentum of the system just after the instant from the perspective of an observer on the ground (c) Determine the [3-d] trajectory of each particle subsequent to the explosion (d)(i) Compute the position(i.e, north, east, up) of each of the fragments (ii) Compute the position of the centre of mass of the fragments at this time. (e)Compute the position that the firework would occupy at t=4s after it reached maximum height had it not exploded.

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ANSWERED

Linda Winkler

Numerade educator

A planar object is bounded above by the curve $y_>=\frac{2}{1+x}$ and below by the line $y_<=\frac{x}{4}$ Assume that the object in homogeneous with constant areal mass-density$\sigma_0$ . (a)Determine the total mass of the object [HINTS: $dm = \sigma_0dxdy $. Do the integrals in two (nested) steps. The y-integrations is from$y_<$to$y_>$ and yields a function of x. The x-integration is from x=0 to x=$16$.] (b)Determine first $M_{Total}X_{CofM}$ and then $X_{CofM}$ . (c) Determine first $M_{Total}Y_{CofM}$ and then $Y_{CofM}$.[Hint: $\int ydy=\frac{1}{2}y^2$]

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ANSWERED

Carson Merrill

Numerade educator

A planar object is bounded by the x and y axes, the curve $y=\frac{2}{1+x}$ and the line $x=e^3-1$ Assume that the object in homogeneous with constant areal mass-density . (a)Determine the total mass of the object [HINTS: $dm = \sigma_0dxdy $. Do the integrals in two (nested) steps. The y-integrations is from y=0 to y=$\frac{2}{1+x}$, and yields a function of x. The x-integration is from x=0 to x=$e^3-1$.] (b)Determine first $M_{Total}X_{CofM}$ and then $X_{CofM}$ . (c) Determine first $M_{Total}Y_{CofM}$ and then $Y_{CofM}$.

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ANSWERED

Linda Winkler

Numerade educator

A planar objectis bounded by the x and y axes, the curve $y=\frac{2}{1+x}$ and the line $x=e^3 -1. $ Assume that the object in homogeneous with constant areal mass-density $\sigma_0$. (a)Determine the total mass of the object (b)Determine first $M_{TOTAL}X_{CofM}$ and then $X_{CofM}$. (c) Determine first $M_{TOTAL}Y_{CofM}$ and then $Y_{CofM}$.

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INSTANT ANSWER

A firework is launched from ground level with speed 65m/s, at 22.62 degrees away from vertical and in the northern direction. At the instant that the firework reaches it's maximum height it explodes into four fragments which fly apart in a horizontal plane. The pieces are labelled N, S, W, E, and their masses and initial velocities as such: Mass Velocity N: 4 2[north] W: 3 -4[east] S: 1 -8[north] E: 2 6[east] (a) Confirm that momentum is conserved just after the instant of the explosion(do this in the frame which is moving with the firework (b)(i) Compute the velocity of each particle, with respect to observers on the ground, just after the instant of the explosion (ii) Compute the total momentum of the system just after the instant from the perspective of an observer on the ground (c) Determine the [3-d] trajectory of each particle subsequent to the explosion (d)(i) Compute the position(i.e, north, east, up) of each of the fragments (ii) Compute the position of the centre of mass of the fragments at this time. (e)Compute the position that the firework would occupy at t=4s after it reached maximum height had it not exploded.

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ANSWERED

Linda Winkler

Numerade educator

consider a force in one-d with magnitude and direction given by F(x)=(-4x^3)+2x. (a)ascertain the points at which the force vanishes (b)Determine the potential energy function associated with this force, whose reference value is U(0)=0. (c)For each of the points in (a), indicate whether a particle located at that point would be "stable" or "unstable." A classical potential energy function applicable to the hydrogen atom and to the solar system has the form U(r)=-(constant)/(r) where r is a radial coordinate and the constant has units of Jm (a)Glossing over the fact that the hydrogen atom and the solar system are fully three-dimensional, determine the form of the conservative force which is associated with this form of potential energy (b)Suppose that a particle subject to the conservative force(in (a)) moves radially inward from ri to rf=ri/2 (i)Under this change in position the potential energy of the particle (increases/decreases/remains the same) (ii)Assuming that no non-conservative forces act while the particle's radial position changes, the kinetic energy of the particle (increases/decreases/remains the same)

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Supratim Pal

Numerade educator

A block of mass m=10kg is pushed along a frictional horizontal plane by an applied force, Fa, in such a way that it moves at a constant speed 3m/s, in the positive x-direction. The coefficient of kinetic friction acting between the block and the plane is mk=1/4. The initial position of the block is ri=(0,0)m, and its final position is rf=(5,0)m. (a)determine the force of kinetic friction acting on the block (b)infer the magnitude and direction of the applied force actin on the block (c)compute the mechanical work done by friction on the block as it moved from its initial to it's final position. (d)compute the mechanical work done by the applied force acting on the block as it is displaced from it's initial to it's final position. (e)compute the power input to the block by: (i)each of the forces individually (ii)the net force

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ANSWERED

Saikat Chatterjee

Numerade educator

A block of mass M is at rest on an inclined plane. The angle of inclination is theta, and the block lies a distance L1 from the bottom. At the bottom of the incline there is a smooth transition to a horizontal plane. At distance L2 away from the base of the incline lies the free end of a spring with force constant k. the other end of the spring is anchored. (a)suppose that the surfaces of the inclined and horizontal planes are frictionless and that the block is released from rest. Determine the maximum compression of the spring. (b)repeat the analysis, incorporating kinetic friction with coefficient mk along the along the ramp and the part of the horizontal plane up to, but not including, that beneath the [uncompressed] spring.

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Anna S.