Help pleasseeee URGENT
1 answer:
Answer:
The speed of the 8-ball is 2.125 m/s after the collision.
Explanation:
<u>Law Of Conservation Of Linear Momentum</u>
The total momentum of a system of masses is conserved unless an external force is applied. The momentum of a body with mass m and velocity v is calculated as follows:
P=mv
If we have a system of masses, then the total momentum is the sum of all the individual momentums:
When a collision occurs, the velocities change to v' and the final momentum is:
In a system of two masses, the law of conservation of linear momentum is simplified to:
The m1=0.16 Kg 8-ball is initially at rest v1=0. It is hit by an m2=0.17 Kg cue ball that was moving at v2=2 m/s.
After the collision, the cue ball comes to rest v2'=0. It's required to find the final speed v1' after the collision.
The above equation is solved for v1':
The speed of the 8-ball is 2.125 m/s after the collision.
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Answer:
The minimum angle at which the box starts to slip (rounded to the next whole number) is α=19°
Explanation:
In order to solve this problem we must start by drawing a sketch of the problem and its corresponding fre body diagram (See picture attached).
So, when we are talking about friction, there are two types of friction coefficients. Static and kinetic. Static friction happens when the box is not moving no matter what force you apply to it. You get to a certain force that is greater than the static friction and the box starts moving, it is then when the kinetic friction comes into play (kinetic friction is generally smaller than static friction). So in order to solve this problem, we must find an angle such that the static friction is the same as the force applie by gravity on the box. For it to be easier to analyze, we must incline the axis of coordinates, just as shown on the picture attached.
After doing an analysis of the free-body diagram, we can build our set of equations by using Newton's thrid law:
we can see there are only two forces in x, which are the weight on x and the static friction, so:
when solving for the static friction we get:
We know the weight is found by multiplying the mass by the acceleration of gravity, so:
W=mg
and:
we can substitute this on our sum of forces equation:
the static friction will depend on the normal force applied by the plane on the box, static friction is found by using the following equation:
so we can substitute this on our equation:
but we don't know what the normal force is, so we need to find it by doing a sum of forces in y.
In the y direction we got two forces as well, the normal force and the force due to gravity, so we get:
when solving for N we get:
When seeing the free-body diagram we can determine that:
so we can substitute that in the sum of y-forces equation, so we get:
we can go ahead and substitute this equation in the sum of forces in x equation so we get:
we can divide both sides of the equation into mg so we get:
as you may see, the angle doesn't depend on the mass of the box, only on the static coefficient of friction. When solving for we get:
when simplifying this we get that:
now we can solve for the angle so we get:
and we can substitute the given value so we get:
which yields:
α=19.29°
which rounds to:
α=19°
