Homework Answers
Yes the marble will exhibit simple harmonic motion (SHM) , because the force pulling it backwards towards the center is constant and equals to= g sin (thetha).
Also the surfaces are frictionless and therefore no energy losses take place .
Thus it will exhibit SHM
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4) A magic marble rolls without friction in a cone-shaped bowl. The marble is at equilibrium...
9. The differential equation for simple harmonic motion (Pr/dt -w22) can be obtained from the expression...
9. The differential equation for simple harmonic motion (Pr/dt -w22) can be obtained from the expression for the total energy of the system. Show that this is true for a mass-spring system. (Hint: consider the total energy equation for this system. What must its time derivative equal) Hint: What are the equations for K and U, and what does the derivative of a constant equal? 10. A small marble slides back and forth in a parabolic bowl without friction. Let...
A "seconds pendulum" is one that moves through its equilibrium position once each second. (The period...
A "seconds pendulum" is one that moves through its equilibrium position once each second. (The period of the pendulum is precisely 2s. The length of a seconds pendulum is 0.992 7 m at Tokyo, Japan, and 0.994 2 m at Cambridge, England. What is the ratio of the free-fall accelerations at these two locations? A simple pendulum makes 120 complete oscillations in 3.00 min at a location where g = 9.80 m/s^2. Find (a) the period of the pendulum and...
4) Figures 4A (side view) and 4B (overhead view) illustrates a uniform solid cylinder having mass M and radius R. The cylinder is positioned on a horizontal floor having sufficient friction to ens...
4) Figures 4A (side view) and 4B (overhead view) illustrates a uniform solid cylinder having mass M and radius R. The cylinder is positioned on a horizontal floor having sufficient friction to ensure that the cylinder can roll without slipping. The cylinder includes a mass-less yoke that is fixed to the symmetric axis of the cylinder and acts as a rolling friction-less pivot for the cylinder. An ideal spring having spring constant K is attached to the yoke at one...
1) A solid ball of mass M and radius R rolls without slipping down a hill...
1) A solid ball of mass M and radius R rolls without slipping down a hill with slope tan θ. (That is θ is the angle of the hill relative to the horizontal direction.) What is the static frictional force acting on it? It is possible to solve this question in a fairly simple way using two ingredients: a) As derived in the worksheet when an object of moment of inertia I, mass M and radius R starts at rest...
Hooke's Law represents a linear restoring force where an elastic system is displaced from equilibrium. In...
Hooke's Law represents a linear restoring force where an elastic system is displaced from equilibrium. In an experiment a rubber band and a spring were placed in a vertical position and a series of having Masses were attached to the free end. a) Does the rubber band used exhibit Hooke's Law behavior? Why or why not? b) Does the spring used exhibit Hooke's Law behavior ? Why or why not? c) Simple Harmonic Motion is oscillatory motion of a system...
4) Figures 4A (side view) and 4B (overhead view) illustrates a uniform solid cylinder having mass...
4) Figures 4A (side view) and 4B (overhead view) illustrates a uniform solid cylinder having mass M and radius R. The cylinder is positioned on a horizontal floor having sufficient friction to ensure that the cylinder can roll without slipping. The cylinder includes a mass-less yoke that is fixed to the symmetric axis of the cylinder and acts as a rolling friction-less pivot for the cylinder. An ideal spring having spring constant K is attached to the yoke at one...
4) A solid uniform sphere mass M an radius R pivots around its center, which is...
4) A solid uniform sphere mass M an radius R pivots around its center, which is rigged to. ntal spring of negligible mass and spring constant k. The sphere rolls without slipping along a horizontal surface. The spring is initially stretched an amount Xmax and is released from rest. Derive an expression for period of the sphere's simple harmonic motion, expressed in terms of the above variables
A cart of mass m rolls without friction on a level surface, and is attached to...
A cart of mass m rolls without friction on a level
surface, and is attached to a light spring of constant k,
the other end of which is attached to a wall. Take the initial
position of the cart, where the spring is neither extended nor
compressed, to be the origin x = 0 of a coordinate system
where positive x values are to the right and positive
vectors point to the right. The cart is pushed to the left...
5. 1/4 points Previous Answers SerPSE10 15.A.P.032 My Notes Ask Your Teacher Two gliders are set...
5. 1/4 points Previous Answers SerPSE10 15.A.P.032 My Notes Ask Your Teacher Two gliders are set in motion on an air track. Glider 1 has mass m = 0.370 kg and moves to the right with a speed 0.810 m/s. It will have a rear-end collision with glider 2, of mass m2 = 0.430 kg, which initially moves to the right with a speed 0.240 m/s. A light spring of force constant 53.0 N/m is attached to the back end...
A region in space contains a total positive charge Q that is distributed spherically such that...
A region in space contains a total positive charge Q that is distributed spherically such that the volume charge density ρ(r) is given by for「SRI2 Here α is a positive constant having units of C/m3 (a) Determine a in terms of Q and R (b) Using Gauss's law, derive an expression for the magnitude of E as a function of r. Do this separately for all three regions. Express your answers in terms of the total charge Q. Be sure...
9. The differential equation for simple harmonic motion (Pr/dt -w22) can be obtained from the expression for the total energy of the system. Show that this is true for a mass-spring system. (Hint: consider the total energy equation for this system. What must its time derivative equal) Hint: What are the equations for K and U, and what does the derivative of a constant equal? 10. A small marble slides back and forth in a parabolic bowl without friction. Let...
A "seconds pendulum" is one that moves through its equilibrium position once each second. (The period of the pendulum is precisely 2s. The length of a seconds pendulum is 0.992 7 m at Tokyo, Japan, and 0.994 2 m at Cambridge, England. What is the ratio of the free-fall accelerations at these two locations? A simple pendulum makes 120 complete oscillations in 3.00 min at a location where g = 9.80 m/s^2. Find (a) the period of the pendulum and...
4) Figures 4A (side view) and 4B (overhead view) illustrates a uniform solid cylinder having mass M and radius R. The cylinder is positioned on a horizontal floor having sufficient friction to ensure that the cylinder can roll without slipping. The cylinder includes a mass-less yoke that is fixed to the symmetric axis of the cylinder and acts as a rolling friction-less pivot for the cylinder. An ideal spring having spring constant K is attached to the yoke at one...
4) Figures 4A (side view) and 4B (overhead view) illustrates a uniform solid cylinder having mass M and radius R. The cylinder is positioned on a horizontal floor having sufficient friction to ensure that the cylinder can roll without slipping. The cylinder includes a mass-less yoke that is fixed to the symmetric axis of the cylinder and acts as a rolling friction-less pivot for the cylinder. An ideal spring having spring constant K is attached to the yoke at one...
4) A solid uniform sphere mass M an radius R pivots around its center, which is rigged to. ntal spring of negligible mass and spring constant k. The sphere rolls without slipping along a horizontal surface. The spring is initially stretched an amount Xmax and is released from rest. Derive an expression for period of the sphere's simple harmonic motion, expressed in terms of the above variables
A cart of mass m rolls without friction on a level
surface, and is attached to a light spring of constant k,
the other end of which is attached to a wall. Take the initial
position of the cart, where the spring is neither extended nor
compressed, to be the origin x = 0 of a coordinate system
where positive x values are to the right and positive
vectors point to the right. The cart is pushed to the left...
5. 1/4 points Previous Answers SerPSE10 15.A.P.032 My Notes Ask Your Teacher Two gliders are set in motion on an air track. Glider 1 has mass m = 0.370 kg and moves to the right with a speed 0.810 m/s. It will have a rear-end collision with glider 2, of mass m2 = 0.430 kg, which initially moves to the right with a speed 0.240 m/s. A light spring of force constant 53.0 N/m is attached to the back end...
A region in space contains a total positive charge Q that is distributed spherically such that the volume charge density ρ(r) is given by for「SRI2 Here α is a positive constant having units of C/m3 (a) Determine a in terms of Q and R (b) Using Gauss's law, derive an expression for the magnitude of E as a function of r. Do this separately for all three regions. Express your answers in terms of the total charge Q. Be sure...
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