We went over the Dynamics Test Review in class today and Mr. Vincent will be posting the answers to the review sometime on Sunday. For fun, I will answer some random review questions and show you how to get the answer.
Practice Problems
5. A grapefruit of mass 0.5 kg is accelerated at 10 m/s². How large is the force acting on it?
Given:
(m) Mass = 0.5 kg
(a) Acceleration = 10 m/s²
(F) =?
F = ma
F = (0.5 kg) (10 m/2²)
F = 5 kg•m/s²
F = +5 N
8. A box is pushed across the floor with a force of 120 N, but experiences a frictional force of 55 N. If the acceleration that results is 1.1 m/s², what is the mass of the box?
Since friction is a resistance to force, the 55 N is subtracted from the applied force to give us the net force.
Fnet = FApplied + FFriction
Fnet = 120N + (-55N)
Fnet = 65 N
We now have force, are given acceleration (1.1 m /s²), and can solve the equation for mass.
F = ma
m = F / a
m = 65 N / 1.1 m/s²
m = 59 kg (2 significant digits)
Conceptual Review
7. A 600-kg car and an 1800-kg truck go from zero to 100 km/h in 10 seconds flat. Calculate the acceleration of each vehicle, including units with your answer. Do they have the same acceleration? Is the same force required to cause this amount of acceleration in each vehicle? Explain using Newton's laws of motion.
First thing to do is convert 100 km/h to meters per second. This is done by dividing by 3.6.
100 km/h
------------ = +27.8 m/s
3.6
Both vehicles reach this speed in 10 seconds, so their acceleration must be the same:
+27.8 m/s ÷ 10s = 2.78 m/s²
Now that we have both vehicles accelerations (2.78 m/s²) and masses, we can solve for the force both vehicles are exerting.
Do they have the same acceleration? Yes, 2.78 m/s
Is the same force required to cause this amount of acceleration in each vehicle? Explain using Newton's laws of motion.
The truck requires more force to accelerate at that rate because it has more mass.
The explanation would come from solving the force for each vehicle using Newton's 2nd law, Force = mass x acceleration:
Truck (1800-kg):
F = ma
F = (1800 kg) (2.78 m/s²)
F = 5004 N
Car (600-kg):
F = ma
F = (600 kg) (2.78 m/s²)
F = 1668 N
The truck needs almost 3x more force than the car to move at 2.78 m/s².
3 comments:
Nice post. Well laid-out answers, for the car and truck question using F=ma is using Newton's second law not his third (third being the action-reaction law). A typo i'm sure.
i think you mennt newton's second law not newtons third law, other wise great job at explaning. :)
Good pickup, Hamida. Great job on the post Robby. Study hard for the test.
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