A small mass of 5g is attached to one end of a light inextensible string of length 20 cm and the other end of the string is fixed. The string is held taut and horizontal and the mass is released. When the string reaches the vertical position, what are the magnitudes of: (a) the kinetic energy of the mass, (b) the velocity of the mass, (c) the acceleration of the mass, (d) the tension in the string? (Neglect air friction.)

A 12N object is attached by a string to a frictionless car that runs along a level track. The car with mass m covers a distance of 1.25 m in 5.0 s after it starts from rest. Find the (a) final speed of the car, (b) loss in potential energy of the 12N object in falling through a distance of 1.25 m, (c) gain in kinetic energy of the car, and (d) mass of the car

tAt time t 0s particle starts moving along the x-axis. If its kinetic energy increases uniformly with time t', the net force acting on it must be proportional to (a) vt (b) constant (c) t (d) 1/ vt

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How much gravitational potential energy (relative to the ground on which it is built) it's stored in an Egyptian pyramid given its mass is about 5×10^9 kg end it center of mass is 24.0 M above the surrounding ground ? j ?  part (b) what is the ratio of this energy to the daily food intake of a person ( 1.2x10^7j) ? :1 ?  I used the ^ to show exponent

At time ti, the kinetic energy of a particle is41.1 J and its potential energy is 11.9 J. Atsome later time tf , its kinetic energy is 18.2 J and 34.8 J for potential energyIf the potential energy at time tf is 7.54 J,what is the work done by the nonconservativeforces acting on the particle?Answer in units of J.

The resilin in the body of a flea has a forceconstant of about 24 N>m, and when the flea cocks its jumpinglegs, the resilin associated with each leg is compressed by approximately 0.12 mm. Given that the flea has a mass of 0.56 mg, andthat two legs are used in a jump, estimate the maximum height aflea can attain by using the energy stored in the resilin. (Assumethe resilin to be an ideal spring.)

A cord is used to vertically lower an initially stationary block of massMat a constant downward acceleration of g/4.When the block has fallen a distance d, find (a) the work done by the cord’s force on the block, (b) the work done by the gravitational force on the block, (c) the kinetic energy of the block, and (d) the speed of the block.

As in the problem above, the particle is projected to the right with initial kinetic energy T, but subject to a force F(x) = -kx + kx'/A", where k and A are positive con- stants. Find (a) the potential energy function V(x) for this force; (b) the kinetic energy, and (c) the total energy of the particle as a function of its position. (d) Find the turning points of the motion and the condition the total energy of the particle must satisfy if its motion is to exhibit turning points. (e) Sketch the potential, kinetic, and total energy func- tions. (Optional: Use Mathcad or Mathematica to plot these functions. Set k and A each equal to 1.) 2.5

It will launch a 25 g projectile to a range of 2.15 m when it is launched at an angle of 45 degrees. You can use this information to find the initial velocity of the ball, of course, (and you should). Therefore, you should be able to calculate how much energy the spring in the projectile launcher must impart to the ball as it is being launched. The ball is pushed back 7.5 cm in the projectile launcher in order to getit ready to fire. What is the spring constant of the projectile launcher?