Physics 101 Problem of the Day
Physics 101 1ST Exam Solutions
1)The figure below shows a position versus time graph for a moving object. The following statements are either true or false. Label each statement as true or false and justify your choice in a sentence using the principles of motion.
a)The object is moving fastest at point H. False, the particle is at rest at H since the slope of the x vs. t curve is zero at H. Slope of x vs. t gives speed.
b)The object is slowing down at point E. True, the slope is changing from a large positive value to zero. Thus the particle is changing its velocity from a large positive velocity coming to rest.
c)The particle is turning around a point C. True, the velocity is changing from large negative to large positive.
d)The object is approaching the origin only at point I. False, the object is also approaching the origin at point D
e)The object is traveling much faster at point B than at point I. False, the slopes at points B and I are about the same indicating the particle has the same speed at both points.
f)The speed of the particle at points F and K are equal. True, the slope of x vs. t is zero at point points F and K, thus the particle is at rest at both points.
g)The acceleration at the point C is negative. False since the velocity is going from a large initial negative value to a large final positive value the acceleration (vf-vi)/Δt will be positive.
h)The acceleration at point H is negative. True, the particle’s velocity is changing from an initial positive to a final negative value. AThus the acceleration will be negative.
i)The average velocity over the entire motion is zero. True, average velocity is defined as Δx/Δt. Since the particle started (Point A) and ended (Point K) at the x=0, the displacement is zero. The average velocity is therefore zero.
2 points each – 18 points total
2)The figure below shows the position graph for an object moving along the horizontal axis. Draw the corresponding velocity graph.
The corresponding velocity curve is
5 points
3)A physics laboratory cart, initially at rest, rolls 2 meters down an inclined plane set on the floor. At the end of the inclined plane, the cart rolls onto the floor and friction brings it gently to a stop 10 meters from the end of the ramp. While the cart is rolling down the inclined plane its acceleration is 0.854 m/s2. While the cart is rolling across the floor it is decelerating at a constant rate.
a)Construct an acceleration versus time graph of the motion.
3 points
b)Construct a velocity versus time graph of the motion.
3 points
c)How long was the cart in motion?
This is a two part problem; two constant acceleration problems. First find the time and final velocity of the cart after acceleration at 0.854 m/s2 down the ramp.
Now find the time to come to rest in 10 meters at a constant deceleration. The simplest way is to recognize that the average velocity on the floor is half the maximum velocity or 0.925 m/s.
The slightly more circuitous method to find the time would be to solve for the acceleration and then find the time.
Thus the cart is in motion for 2.16 s + 10.8 s = 13.0 s.
6 points
4)A car traveling at a velocity of 50 m/s takes 175 m to stop after the brakes are applied. What velocity must the same car have to stop in 100 m? Assume the same acceleration.
This problem is most elegantly answered using a ratio technique. It can also be solved by the calculation of the acceleration.
Since the accelerations are equal in the problem we can write that
Solve this proportion for v2
Now fill in the numbers…
The car must have a velocity of 37.8 m/s to stop in 100 meters.
6 points
5)A puppy runs out of the front door of the house first thing in the morning and heads 15 m south to urinate in his favorite spot. He then races 30 m west across the lawn chasing a rabbit. As puppies do, he is distracted from the rabbit by the cat and turns northeast chasing the cat for 10 m where upon he is called from the front door for breakfast breaks off the cat chase and heads directly to the door.
a)Construct an approximate vector diagram showing the displacement vectors of the puppies run.
4 points
b)How far did the puppy run in total?
To answer this question we simply add the displacements in each of the vectors above. However, we must first find the displacement of the last “sprint for breakfast vector. We accomplish this by vector adding the first three legs of the journey component-wise and then finding the magnitude of that summation vector.
The “breakfast sprint has a magnitude of 24.3 meters, so the total displacement of the puppy is 15 m+30 m+10 m+24.3 m = 79.3 m.
4 points
6)According to Wikipedia, the free encyclopedia, Thrust SSC (SuperSonic Car) is a British-designed and built jet-propelled car developed by Richard Noble, Glynne Bowsher, Ron Ayers and Jeremy BlissThrust SSC holds the World Land Speed Record, set on October 15, 1997, when it achieved a speed of 341.1m/s (763mph) and became the first car to officially break the sound barrier. The car was driven by Royal Air Force fighter pilot Squadron Leader Andy Green in the BlackRockDesert in Nevada, United States. It was powered by two afterburning Rolls-Royce Spey turbofan engines, as used in British F-4 Phantom II jet fighters. It is 16.5m long, 3.7m wide and weighs 101,600 N. The engines developed a thrust of 223,000N, a power output of 82 million Watts and burned around 4.8 US gallons/s.
a)What is themass of the SSC?
Mass is given from the expression for weight, Weight = mg. Therefore, the mass is just
2 points
b)Draw a free body diagram of forces on the SSC when it is in motion. Assume, unrealistically, no air resistance.
2 points
c)Describe the NET force on the SSCin magnitude and direction.
The NET force is just the thrust since the two vertical forces (Normal and Weight) must cancel out. If the vertical forces did not cancel out then there would be acceleration in the vertical direction.
2 points
d)What is the acceleration of the SSC?
The acceleration in given by Newton’s 2ND law: F=ma. Solve for a, where F is the thrust of the engines, 223,000 N from the problem, and the mass is 10,370 kg from part (a).
The SSC accelerates at 21.5 m/s2.
2 points
e)How long will it take the engines to get the SSCmoving to its top speed?
About 15.9 s is required by the SSC to reach the top speed of 341.1 m/s, assuming a constant acceleration of 21.5 m/s2.
2 points
f)Could the SSC reach its top speed on a 1 mile-long straight (1,600 m) track?
The SSC could only reach a speed of 262.3 m/s on a mile track. This is almost 79 m/s short of its top speed.
2 points
61 points total. Class results appear below.
