PHY451H5 Chapter Notes - Chapter 1-2: Equations For A Falling Body, Centripetal Force

vf = vi + at
rx = vit + ½ at2
vf2 = vi2 +2arx
rx = ½ (vi + vf)t

4. A sailboat is moving across the water at 3.0 m/s. A gust of windfills its sails and it accelerates at a constant 2.0 m/s2. At thesame instant, a motorboat at rest starts its engines andaccelerates at 4.0 m/s2. After 3.0 seconds have elapsed, find thevelocity of (a) the sailboat, and (b) the motorboat.



7. A rail gun uses electromagnetic energy to accelerate objectsquickly over a short distance. In an experiment, a 2.00 kgprojectile remains on the rails of the gun for only 2.10x10-2 s,but in that time it goes from rest to a velocity of 4.00×103 m/s.What is the average acceleration of the projectile?



12. A space shuttle sits on the launch pad for 2.0 minutes, andthen goes from rest to 4600 m/s in 8.0 minutes. Treat its motion asstraight-line motion. What is the average acceleration of theshuttle (a) during the first 2.0 minutes, (b) during the 8.0minutes the shuttle moves, and (c) during the entire 10 minuteperiod? (be careful with min and seconds)



19. The United States and South Korean soccer teams are playing inthe first round of the World Cup. An American kicks the ball,giving it an initial velocity of 3.6 m/s. The ball rolls a distanceof 5.0 m and is then intercepted by a South Korean player. If theball accelerates at -0.50 m/s2 while rolling along the grass, findits velocity at the time of interception.




23. The city is trying to figure out how long the traffic lightshould stay yellow at an intersection. The speed limit on the roadis 45.0 km/h and the intersection is 23.0 m wide. A car istraveling at the speed limit in the positive direction and canbrake with an acceleration of -5.20 m/s2. (a) If the car is to stopon the white line, before entering the intersection, what is theminimum distance from the line at which the driver must apply thebrakes?



**(b) How long should the traffic light stay yellow so that if thecar is just closer than that minimum distance when the light turnsyellow, it can safely cross the intersection without having tospeed up?

I no this is alot of questions but im having trouble answeringthese! So please help me..

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?

MAC, Inc. (the company you work for) has decided to move forwardwith a feasibility
study for a product it wishes to manufacture and sell. This productis a particle launcher that should have the capability, for everyactivation, of launching two particles into the air at twodifferent times and at two different angles of elevation, in anautomated fashion so that they both land at the same distance fromthe launch point at the same time. For example, let P1 and P2 betwo particles, let T1 and T2 be two times, and let theta1 andtheta2 be two angles of elevation. Once activated, the launchershould be able to operate so that particle P1 is launched at timeT1 with an angle of elevation theta 1, and particle P2 islaunched
at time T2 with an angle of elevation theta2.
The launcher must be configured by a technician, prior to eachactivation, so that the
initial speed is set for the launcher, and the distance from thelauncher to where both
particles will land is set. For each activation of the launcher,the initial speed will be the
same for both particles. Once the technician has set the initialspeed and desired distance,
the launcher must calculate the angles of elevation to use and howmuch time to wait in
between particle launches. Then, when the technician activates thelauncher, both
particles will be launched at the appropriate angles of elevationand at the appropriate
times so that they both land at the configured distance from thelauncher at the same time.
The launcher, based on its calculations, will change the angle ofelevation to be ready for
the second particle launch. The launcher, however, must flash awarning for the
technician if the information the technician used to configure thelauncher does not result
in a two-particle launching solution.
Certain assumptions must be made. It is assumed that that launchercan always change
the angle of elevation to get ready for the second particle launchfaster than the time
delay calculated for the second particle launch. It is assumed thatthe units for speed are
meters per second, that the units for distance are meters, and thatgravity is 9.8 meters per
second squared. It is assumed that gravity is the only force actingon the motion of the
particles after launch, and that there is no wind to be considered,so that the particles land
at a point exactly in line with the direction the launcher ispointed.
The questions that must be answered and written up in anengineering report are as
follows:
1. Given the initial speed and desired landing distance for theparticles, find the
mathematical expressions that must be used to find 1, 2, and thetime delay
between particle launches.
2. Determine under which conditions the launcher will not be ableto perform the
operation requested, and will consequently flash a warning to thetechnician.
3. Each particle launched will follow a path of motion that isparabolic. Show that
the vertex of the parabola for each particle’s path occurs at thesame distance from
the launcher.
4. Along the path of each launched particle, there will be amaximum curvature.
Find that maximum curvature for each launched particle.