b) Two skaters collide and grab on to each other on a frictionless ice. One of them, of mass 80 kg, is moving to the right at 5.
1 answer:
Answer:
The two skaters move with a speed of 1.73 m/s after the collision in the right direction.
Explanation:
Given that,
The mas of skater 1, m₁ = 80 kg
The speed of skater 1, u₁ = 5 m/s (right)
The mass of skater 2, m₂ = 70 kg
The speed of skater 2, u₂ = -2 m/s (left)
Let v is the magnitude of the two skaters just after they collide. They must have a common speed. So, using the conservation of momentum as follows :
Put all the values,
So, the two skaters move with a speed of 1.73 m/s after the collision in the right direction.
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Answer:
The acceleration of the crate is 1.8 m/s² so the answer is a.
Explanation:
The very first thing you must do when solving this problem is to draw a free body diagram. (The body diagram is attached to this answer)
So once we got the free body diagram, we can analyze it and build our sum of forces in the x and y directions. Notice that according to the diagram, there are 4 forces to this problem, Normal (N), Weight (W), kinetic friction (fk) and the 750N force.
As one may see in the free body diagram, two of the forces are vertical forces: N and W, so we can use them to build a sum of forces:
Starting with the sum of forces in the y-direction, we get:
Σ=0
We set the sum equal to zero because there is no movement in the y-direction, so the system is in vertical equilibrium.
so the sum will be:
when solving for N we get that:
N=W
where W is found by multiplying the mass of the crate by the acceleration of gravity:
N=250kg*9.8m/s²
N=2450N
Once we found the normal force, we can use it to find the kinetic friction which is given by the following formula:
μ
where μ is the kinetic friction coefficient.
So we get that the kinetic friction is:
so
With this information we can go ahead and find the sum of horizontal forces:
Σ=ma
In this case the sum is equal to mass times acceleration because the crate is moving horizontally due to the action of a force, so it will have an acceleration.
so the sum of forces look like this:
750N-=ma
so
750N-294N=(250kg)a
when solving for a we get:
so the crate's acceleration is 1.82m/s².
Here We can use principle of angular momentum conservation
Here as we know boy + projected mass system has no external torque
Since there is no torque so we can say the angular momentum is conserved
now we know that
m = 2 kg
v = 2.5 m/s
L = 0.35 m
I = 4.5 kg-m^2
now plug in all values in above equation
so the final angular speed will be 0.37 rad/s