Motion (speed, acceleration, free fall, etc )

[ashx]

Hi everyone! I have 7 questions here, I completed them all, but I’m not sure if I got them correct. I would greatly appreciate it if someone could have a look at them and let me know if I need to fix anything - I had the most trouble with question 3. Thank you so much for your time!

Speed

1.) How many minutes would you save by making a 100Km trip at 125Km/h instead of 80Km/h?

v = d/t Therefore t = d/v

t₁ = (100Km) / (125Km/h), t₁ = 0.8h
t₂ = (100Km) / (80Km/h), t₂ = 1.25h

(1.25h) – (0.8h) = 0.45h

(0.45h) * (60) = 27 minutes saved.

Acceleration

2.) The tires of a car begin to lose their grip on the road at an acceleration of 5m/s². At this acceleration, how long does the car need to reach a speed of 25m/s starting from 10m/s?

a = v₂ – v₁ /t Therefore t = v₂ – v₁ /a

(25m/s) – (10m/s) / (5m/s²) = 3 seconds.

Free Fall

3.) A rifle is aimed directly at a squirrel in a tree. Should the squirrel drop from the tree at the instant the rifle is fried or should it remain where it is? Why?

Ok, let’s call the squirrel Ned. I think that the smartest thing Ned could do is stay right where he is, because the bullet won’t hit him directly because gravity is pulling down on it, so if he jumped, he would be jumping into the bullet. But I was talking to someone and they said that gravity won’t pull on the bullet right away because is going so fast, so Ned should drop down. And then the more I thought about it, the more confused I got, because the question doesn’t say how far away the shooter is. So if he was close, it would make sense for Ned to drop, but if he was further away, then Ned shouldn’t move. But then does it really matter? Because the bullet is supposedly going fast enough that it’s going to end up hitting him anyways. Arrg!

4.) A ball is thrown upward at 12m/s. What is its speed 1.0s later?

a = v₂ – v₁ /t Therefore v₂ = v₁ + at

(12m/s) + (-9.8m/s²) * (1.0s) = 2.2m/s, upward.

I’m not too sure if it's supposed to be +9.8m/s², or -9.8m/s².

2nd Law of Motion

5.) A car as a maximum acceleration of 4m/s². What is its maximum acceleration when it is towing another car with the same mass?

From my text, it says: “For the same net force, doubling the mass cuts the acceleration in half.” So in that case, the car’s maximum acceleration would be 2m/s².

Circular Motion

6.) The greatest force a road can exert on the tires of a certain 1400Kg car moving at 25m/s is 8kN. What is the minimum radius of a turn the car can make without skidding?

Fc = mv² /r Therefore r = mv² /Fc

8kN = 8000N

(1400Kg) * (25m/s)² / 8000N

875000(Kg)(m/s²) / 8000N

109.375m

I'm actually not too sure what unit that is supposed to be, or how I got it. I was assuming since they wanted the radius, it would be in meters.

Newton’s Law of Gravity

7.) If the moon were twice as far from the Earth as it is today, how would the gravitational force it exerts on the Earth compare with the force it exerts today?

I’m not too sure if this is correct, but my text it says:
“The gravitational force between two objects depends on their masses and the distance between them.
- All objects attract with a force proportional to both their masses and
- Inversely proportional to the square of the distance between them"

And then this equation followed:

1 /R²

so

1/ 2² = 1/4

The moon would exert a quarter of its original force. I think. I originally thought it would have been half the force.

 

[gabbagabbahey]

Hi everyone! I have 7 questions here, I completed them all, but I’m not sure if I got them correct. I would greatly appreciate it if someone could have a look at them and let me know if I need to fix anything - I had the most trouble with question 3. Thank you so much for your time!

All of your solutions are correct.

For #3, the squirrel should stay right where it is because according to Newton's law of gravitation, all objects fall at the same rate regardless of what their mass is (neglecting air resistance of course) and so if the squirrel were to let go, it would fall at the same rate as the bullet and get hit.

For #4, -9.8 m/s^2 is the correct value to use, because the force of gravity will slow down (decelerate) the ball and so a must be negative if v_initial is positive.

For # 6 the units are meters because
$$1N=1 \frac{kg m}{s^2}$$

 

[baba89]

Hi there! It looks like you have a good understanding of the concepts of speed, acceleration, and circular motion. I'll go through each question and provide my feedback:

1. Your calculations and method for finding the time saved are correct. However, I would suggest including the units in your final answer, so it would be "27 minutes saved."

2. Your calculations and method for finding the time needed are correct.

3. You are correct in saying that the squirrel should stay where it is. This is because gravity will not have enough time to pull the bullet down significantly before it reaches the squirrel. The distance between the shooter and the squirrel does not matter in this case.

4. Your calculations are correct, and the acceleration due to gravity should be negative as it is acting in the opposite direction of the initial velocity.

5. Your understanding of the second law of motion is correct, and your answer of 2m/s² is also correct.

6. Your calculations and method for finding the minimum radius are correct. The unit should be in meters, so your final answer would be 109.375m.

7. Your understanding of the inverse square law is correct. The moon would exert a quarter of its original force if it were twice as far from the Earth. This means that it would have half the gravitational pull compared to its current distance. So your original thought of half the force was correct.

Overall, your understanding and calculations are correct. Keep up the good work!