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- Q2/ Suppose we are told that the acceleration a of a particle moving with uniform speed v in a circle of radius r is proportional to some power of r, say r. and some power of v, say v", also some power of mass, say mº. Determine the values of n and m and o.Q1. A driver enters a curved car at 72 km/h, slows down, causing the speed to drop at a steady rate of 4.5 km/h every second. If the radius of curvature is 16.7 m. Find the acceleration of the car after 4 seconds from the driver starting to slow down.1. A truck undergoes an acceleration of 0.25m/s2. If its wheels are 1.0 meter in a diameter, what is their angular acceleration? 2. A record is dropped on a turntable rotating at 33.5 rpm. The record slips briefly before reaching the same speed as the turntable. If the turntable rotates through 20 degrees while the record is slipping, find the record's angular acceleration.
- Q1 A balloon is rising vertically above a level, straight road at a constant rate of 2 ft sec. Just when the balloon is 60 ft above the ground, a bicycle moving at a constant rate of 17 ft sec passes under it. How fast is the distance s(t) between the bicycle and balloon increasing 3 sec later?1. The wheel starts rotating from rest, 4) if its angular velocity W as a function of angular position 0 is w=0.1-0², where O is in radian, and its radius ris 0.2 m, what is the magnitude of the normal linear acceleration (in m/s2) of point Pafter the wheel has turned 1.1 revolution(s) from rest. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. Your Answer: Answer2. A car accelerates uniformly from rest and reaches a speed of 28.0 m/s in 8.00 s. If the radius of a tire is 30 cm, find the number of revolutions the tire makes during this motion, assuming that no slipping occurs.
- 3. An engineer is designing the runway for an airport. Of the planes that will use theairport, the lowest acceleration rate is likely to be 3 m/s2. The takeoff speed forthis plane will be 65 m/s. Assuming this minimum acceleration, what is the minimum allowed length for the runway?The elevator in an office building, starting from rest at the first floor, is accelerated 0.75 m/sec2 for 5 secs. It continues at constant velocity for 12 secs, more and is then stopped in 3 secs with constant deceleration. If the floors are 3.75 m apart, at what floor did the elevator stop?A pendulum in your house swings from one side to the other in a span of 0.8 seconds. If this pendulum will be brought to moon, how long should the string be in meters to maintain the same period? Acceleration due to gravity at moon is 1.62m/s2 A pendulum in your house swings from one side to the other in a span of 0.8 seconds. If this pendulum will be brought to Mars, how long will the new period be in seconds? Acceleration due to gravity at Mars is 3.7m/s2 A pendulum in your house swings from one side to the other in a span of 0.8 seconds. How long is the string that is attached to the mass? A particle moves with a simple harmonic motion through space. When time was zero, its position was at the equilibrium position with a 15cm/s velocity. What is its velocity in cm/s after 5 seconds? The object is vibrating at 3.5pi rad/s A particle moves with a simple harmonic motion through space. When time was zero, its position was at the equilibrium position with a 15cm/s velocity. What…
- In class, we used the 1967 gravity formula to derive the change in gravitational acceleration g with latitude, and we calculated the result at latitude o = 45°. Plot the rate of change of g with latitude () in units of mgal/km, from the equator to the pole (ø = 0° to ø = 90°). Be careful with the units; you will need to convert radians to km. (Recall that there are 27 radians in a full circle, 360°.) do1. The wheel starts rotating from rest, 5) if its angular velocity W as a function of angular position is w=0.2-0², where 0 is in radian, and its radius ris 0.3 m, what is the magnitude of the total linear acceleration (in m/s2) of point P after the wheel has turned 1.4 revolution(s) from rest. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. Your Answer: Answer P2. Connor lives on a steep hill and wants to conduct a Dynamics experiment with his car. He starts from rest at the top of the hill and releases the brakes. His acceleration down the grade is a function of velocity and is described by the equation a = 3.22 0.04v² where v is the velocity of his car in ft/sec. Predict the velocity of Connor's car at the bottom of the grade in mph. [Ans. to check: 6.12 mph] A 600¹ V