A ball bearing with a mass of .0792 kg is released at teh top ofa 1.63 m Galileo Track raised to an angle of 75.0 degrees above thehorizontal at .4 m/s, which has a coefficient of friction of .250.When it reaches the bottom of the track, it collides with a secondball bearing with a mass of .950 kg in a two-dimensional collision.Calculate the energy lost due to non-conservative forces during thecollision of the two ball bearings.

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Nestor RutherfordLv2

13 Jul 2019

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1. An object of mass 19 kg is placed on incline with friction.The incline is originally horizontal and then raised slowly and at21 degrees, the mass begins to slide down the incline. It is foundthat the coefficient of kinetic friction is 0.79 times thecoefficient of static friction. If the same object (same mass) isplaced on the same incline with an inclination angle of 42.2degrees (the mass will slide down the incline at this angle), whatis the magnitude of the acceleration on the mass in m/s2?
2. A mass enters the bottom of a 50 degree incline with acoefficient of kinetic friction of 0.6. At the bottom of theincline the mass is moving at 33 m/s and is moving up the incline.After the mass has traveled, 25 meters up the incline, what is themagnitude of its velocity in m/s?
3. A car is traveling around a circular, banked track withoutfriction. It is initially traveling around the bottom of the ramp(on the ground) where the inner radius of track is 351 meters. Thecar then increases its velocity by a factor of 1.7. If theinclination angle is 10 degrees, what is the height (verticaldistance above the ground) the car is traveling at this newvelocity. Answer in meters.
4. An yo-yo with a mass of 2.4 kg is swung in a vertical circle. Itis found that the string breaks at 228 Newtons. If its the yo-yo'sspeed is a constant and is the maximum speed the yo-yo can movebefore the string breaks, what is the the tension in the string atthe top of the circle in Newtons?
5. A roller coaster cart of mass 15.8 kg travels on the inside of aroller coaster track in a loop of radius 23.1 meters. The circle isa vertical circle similar to the yo-yo example done in class. Ifthe cart travels at a constant speed around the track and the valueof this speed is the minimum speed such that cart does not fall offthe track at the top of the track, was is the magnitude of thenormal force on the cart at the bottom of the track in Newtons?

Some Problems on Work
1. Joe is pulling a box of mass m = 10 kg up an inclined surface (?= 30degrees) using
a rope. The coefficient of kinetic friction between the surface andthe box is
Âµk = 0.5. It takes 10 seconds for Joe to bring up a box at aconstant velocity
V = 0.8m=s.
(a) What is the tension of the rope?
(b) What is the work done by the tension?
(c) What is the work done by the normal force?
(d) What is the work done by gravity?
(e) What is the total work done on the box?
(f) What is the power output necessary to Joe to bring up thebox?
maximal compression of the spring?
2. A block (m=50 kg) slides down a 3 m long inclined surface (? =30). The
coefficient of kinetic friction between the block and the surfaceis Âµk = 0.3.
Calculate the nal velocity of the block using the work-energytheorem.
3. A pendulum of length l and mass m is released from rest at anangle ? from
the equilibrium position.
(a) Neglect air friction. Calculate the velocity of the pendulumwhen the angle
is zero. Express your result in terms of ?, l, and m.
(b) Suppose ? = 60 degrees and l = 1 m. Suppose that the velocityof the pendulum
when the angle is zero is 1 m/s. Calculate the work done by the airfriction.
4. A point particle of mass m = 20 g is moving on a
at
surface when it reaches a slope which brigs it up by h = 08 m. Thespeed of
the particle in position A is v = 5 m/s.
(a) Suppose that there is no friction. What is the velocity of theparticle when
it reaches position B?
(b) Suppose that there is friction, and that the velocity of theparticle in B is
0. What is the work done by the friction from A to B?
5. A ball is shoot vertically with initial speed v, from a
table of height h.
(a) Calculate the maximal height ymax that the ball can reach (b)Calculate the velocity of the ball just before it hits thefloor.

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