Newton’s Laws
Applications of Newton’s Law
Problems –
1D Kinematics
Average velocity
1.Train A starts at 4 miles South of a bridge and heads North at a constant speed of 30 miles per hour. Train B starts 6 miles North of the bridge.
a. What velocity must Train B have so that the two trains cross the bridge at the same time?
b. If Train B goes at 35 miles per hour, South, how far away from the bridge do they cross?
2.A person goes out for a bike ride to a nearby town. A record of the trip is as follows: 30 minutes at 30 km/hour, 15 minutes at 40 km/h, 5 minutes at 0 km/h for a break, and 20 minutes at 15 km/h.
a. What is the distance the person traveled?
b. What is the average velocity?
3.After a road trip on I-5 you realize exactly half of the time you were driving 65 miles per hour and the other half at 10 miles per hour in a Portland traffic jam.
a. What was your average speed?
b. What if you were traveling at each speed for the same distance instead of time... What would your average speed be then, if different?
Accceleration
4.Rumor has it, that upon the building's completion, a certain physics faculty member contributed significantly to our understanding of gravitation and its effects on large fruit by dropping a watermelon off Willamette Hall's top floor (not reccommended). Given that it took 2 seconds before it impacted the floor, from how far off the ground was it dropped?
5.You are asked to do an experiment to measure g. You set up a device which drops a metal ball from rest from a height of 1.650m. Using an accurate timing device which detects the release of the ball and its landing on the floor, you measure the average time of the falling ball to be 0.585s.
a. What do you measure the value of g as?
b. Can you give an explanation as to the error from the accepted value of 9.8 meters per square second?
6.A car increases its velocity from 15 m/s to 25 m/s in the distance of 20 m.
a. Find the magnitude of this acceleration
b. Find the time it takes for the car to travel this distance
7.A person is stuck inside a falling elevator, whose cable broke 10 meters above the ground. Lets say the person wanted to cancel out their final velocity by jumping exactly when the elevator hits bottom. Assume the elevator started from rest.
a. How long after the cable breaks would the person need to jump?
b. In order to completely cancel their accumulated velocity, at what velocity (relative to the elevator) would they need to jump?
c. If they were to jump at this velocity on stable ground, how high would they go? Is this reasonable?
8.Automobile experts will often refer to a car's "0 to 60 time", the time it takes for a car to go from rest to 60 miles/hour, when talking about how powerful its engine is. For example, a Ferrari Daytona's "0 to 60 time" is about 6 seconds.
a. What is the acceleration of this car compared to that of gravity?
b. If you had a car able to accelerate at 1 g, what would its "0 to 60 time" be?
9.A model rocket is launched from rest and its engine delivers a constant acceleration of 8.2 meters per square second for 5.0s after which the fuel is used up. Assuming the rocket was launched straight up into the air,
a. Find the maximum altitude reached by the rocket.
b. Find the total time the rocket is in flight.
assume no air resistance
10.A basketball is dropped from a height of 2.00 meters above the ground. On the first bounce the ball reaches a maximum height of 1.10 meters where it is caught. Find the velocity of the ball:
- just before it makes contact with the ground
b.just after it leaves the ground after the bounce
Also, find the total time from drop to catch (neglecting the time the ball is in contact with the ground)
And, just for fun, how much energy is lost during the bounce? Assume the ball weighs 0.2 kg.
11.A watermelon is dropped with an initial velocity equal to zero from the top of a 20.0m cliff. At the same time, a person at the bottom of the cliff shoots an arrow up towards the watermelon. The arrow strikes the watermelon after 0.300 seconds.
- How far up the cliff does the arrow strike the watermelon?
- What was the arrow's initial velocity?
12.A ball is thrown straight up in the air and passes a certain window 0.30s after being released. It passes the same window on its way back down 1.50s later. What was the initial velocity of the ball?
Multi-dimensional kinematics
13.A baseball (m=0.15kg) is thrown with a speed of 30 meters per second at angle of 32 degrees above the horizontal. Neglect air resistance.
a. What is its momentum at the maximum height?
b. What is its momentum just before it strikes the ground?
Remember that momentum is a vector, so you need to find the magnitude AND the direction that it is pointing in
14.The farthest a person can throw a ball with no air resistance ( ) is s.
a. If they threw the ball with the same initial speed, but straight up, how high would it go as a fraction of s?
b. If the max distance were 60.0m, what would be the max height?
15.A football is thrown to a moving football player. The football leaves the quaterback's hands 1.5m above the ground with a speed of 15 m/s at an angle 25 degrees above the horizontal. If the receiver starts 10m away from the quarterback along the line of flight of the ball when it is thrown, what constant velocity must he have to get to the ball at the instant it is 1.5m above the ground?
16.You have a machine that launches a brick at a speed , above the horizontal. You can use this device to measure the height of a building.
a. Given , and the distance d that the brick lands from the building, find an equation for the height h of the building in terms of , , and d.
b. You use this machine set at initial speed 10. meters per second and = 30 degrees. You find that the brick lands 18m away from the base of a building. How high is it?
17.A plane with supplies is at an altitude h a distance over ground x from its drop point and the nose makes an angle below horizontal.
a. What speed must the plane have at that moment to be able to release its supplies and have them land right on the drop zone?
b. When does this equation blow up (what are the limits of the variables)? Why?
Ignore air resistance and consider to be the direction of the velocity of the plane.