Satellite and gravity

1. Show by algebraically reasoning that your gravitation acceleration towards an object of mass M a distance d away is a=GM/d^2 and therefore doesn't depend on your mass. 2. Can a satellite coast in a stable orbit in a plan that doesn't intersect the earth center? Defend your answer. (Include 1 or more diagrams) 3. Stude ...continues

kinetic energy

"On a frozen pond, a 10.6 kg sled is given a kick that imparts to it an initial speed of V(0) = 1.73 m/s. The coefficient of kinetic friction between the sled and the ice is mu(k) = 0.102. Use the work-kinetic energy theorem to find the distance the sled moves before coming to rest."

KE, average speed

"A 48.5 kg student climbs a 5.90 m long rope and stops at the top. What must her average speed be in order to match the power output of a 140 W lightbulb?" Here's how I approached this problem: Since 1 W = 1 J/s, I set KE = 140 J. Then, v^2 = KE/((.5)m) = 140/24.25 = 5.77 Then v = 2.4 m/s But that's not the right an ...continues

Spring action

"The launching mechanism of a toy gun consists of a spring of unknown spring constant. If the spring is compressed a distance of 0.139 m and the gun is fired vertically, the gun can launch a 25.1g projectile from rest to a maximum height of 24.5 m above the starting point of the projectile. Neglecting all resistive forces, deter ...continues

Spring action

"The launching mechanism of a toy gun consists of a spring of unknown spring constant. If the spring is compressed a distance of 0.139 m and the gun fired vertically, the gun can launch a 25.1g projectile from rest to a maximum height of 24.5 m above the starting point of the projectile. Neglecting all resistive forces, determin ...continues

Springs and Forces

A spring of negligible mass stretches 3.00 cm from its relaxed length when a force of 6.20 N is applied. A 1.200 kg particle rests on a frictionless horizontal surface and is attached to the free end of the spring. The particle is pulled horizontally so that it stretches the spring 5.00 cm and is then released from rest at t=0. ...continues

Springs and Forces

A child's toy consists of a piece of plastic attached to a spring. The spring is compressed against the floor a distance of 2.00 cm, and the toy is released. If the toy has a mass of 90 g and rises to a maximum height of 50.0 cm, estimate the force constant of the spring (in N/m). I need help on which equation/formula to use a ...continues

spring constant of bungee cord

"A 61.2 kg bungee jumper jumps from a bridge. She is tied to a 11.2 m long (unstretched) bungee cord and falls a total of 32.4 m. Calculate the spring constant k of the bungee cord." Here's how I approached this question: (1/2)(k)(x^2) = mgH k = 2mgH/x^2 k = (2)(61.2)(9.8)(32.4)/11.2^2 = 309.8 N/m But this is not the ...continues

KE/PE

"In the high jump, the kinetic energy of an athlete is transformed into gravitational potential energy without the aid of a pole. With what minimum speed must the athlete leave the ground in order to lift his center of mass 2.00 m and cross the bar with a speed of 0.670 m/s?" Thank you!

Energy lost due to friction

"A 25.0 kg child slides down a long slide in a playground. She starts from rest at a height h1 of 20.00 m. When she is partway down the slide, at a height h2 of 8.00 m, she is moving at a speed of 8.90 m/s. Calculate the mechanical energy lost due to friction (as heat, etc.)."