Answer
The answer and procedures of the exercise are attached in the following archives.
Step-by-step explanation:
You will find the procedures, formulas or necessary explanations in the archive attached below. If you have any question ask and I will aclare your doubts kindly.
Answer:
Explanation:
In order to solve this problem, we must first do a drawing of the situation (see attached picture).
When the brakes of the car were applied, we can see that there was only one horizontal force affecting the vehicle's movement, which was the force of friction. When analyzing the free body diagram we can apply Newton's laws to determine the equations we will use to solve this.
so:
-f=ma
we also know that:
so
we can now solve for the acceleration, so we get:
we don't know what the normal force is, so we can find it out by analyzing the vertical forces applied to the car:
so we get:
N-W=0
which means that:
N=W
we also know that:
W=mg
so
N=mg
we can substitute this into the first equation so we get:
which simplifies to:
we can now substitute the provided data:
which yields:
once we got the acceleration, we can use kinematics formulas to solve this, we got the following formula:
we know the final velocity must be zero, since that's where the car got to a stop, so the formula then becomes:
we can now solve for the initial velocity, which yields:
so we can now substitute the daa we know, so we get:
so we get:
So from this we know that the velocity of the car must have been of at least 29.68m/s when the brakes were applied.
Answer:
The spring constant of the spring is 47.62 N/m
Explanation:
Given that,
Mass that is attached with the spring, m = 29 g = 0.029 kg
The spring makes 20 complete vibrations in 3.1 s. We need to find the spring constant of the spring. We know that the number of oscillations per unit time is called frequency of an object. So,
f = 6.45 Hz
The frequency of oscillator is given by :
k is the spring constant
k = 47.62 N/m
So, the spring constant of the spring is 47.62 N/m. Hence, this is the required solution.