If a train is going 60 m/s hits the brakes, and it takes the train 1 minute 25 seconds to stop, what is the train’s acceleration
1 answer:
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Answer:
The force of friction acting on block B is approximately 26.7N. Note: this result does not match any value from your multiple choice list. Please see comment at the end of this answer.
Explanation:
The acting force F=75N pushes block A into acceleration to the left. Through a kinetic friction force, block B also accelerates to the left, however, the maximum of the friction force (which is unknown) makes block B accelerate by 0.5 m/s^2 slower than the block A, hence appearing it to accelerate with 0.5 m/s^2 to the right relative to the block A.
To solve this problem, start with setting up the net force equations for both block A and B:
where forces acting to the left are positive and those acting to the right are negative. The friction force F_fr in the first equation is due to A acting on B and in the second equation due to B acting on A. They are opposite in direction but have the same magnitude (Newton's third law). We also know that B accelerates 0.5 slower than A:
Now we can solve the system of 3 equations for a_A, a_B and finally for F_fr:
The force of friction acting on block B is approximately 26.7N.
This answer has been verified by multiple people and is correct for the provided values in your question. I recommend double-checking the text of your question for any typos and letting us know in the comments section.
Answer:
a) vd = 47.88 m/s
b) θ = 80.9°
c) t = 6.8 s
Explanation:
In the situation of the problem, you can assume that the trajectory of the hawk and the trajectory of the mouse form a rectangle triangle.
One side of the triangle is the horizontal trajectory of the hawk after 2.00s of flight, the other side of the triangle is the distance traveled by the mouse when it is falling down. And the hypotenuse is the trajectory of the hawk when it is trying to recover the mouse.
(a) In order to calculate the diving speed of the hawk, you first calculate the hypotenuse of the triangle.
One side of the triangle is c1 = (18.0m/s)(2.0s) = 36m
The other side of the triangle is c2 = 230m - 3m = 227 m
Then, the hypotenuse is:
(1)
Next, it is necessary to calculate the falling down time of the mouse, this can be done by using the following formula:
(2)
yo: initial height = 230m
vo: initial vertical speed of the mouse = 0m/s
g: gravitational acceleration = -9.8m/s^2
y: final height of the mouse = 3 m
You replace the values of the parameters in (2) and solve for t:
The hawk traveled during 2.00 second in the horizontal trajectory, hence, the hawk needed 6.8s - 2.0s = 4.8 s to travel the distance equivalent to the hypotenuse to catch the mouse.
You use the value of h and 4.8s to find the diving speed of the hawk:
The diving speed of the Hawk is 47.88m/s
(b) The angle is given by:
Then angle between the horizontal and the trajectory of the Hawk when it is descending is 80.9°
(c) The mouse is falling down during 6.8 s