Respuesta :
Answer:
Explanation:
Given
mass of puck=166 gm
initial velocity=19.5 m/s
Final velocity=43.1 m/s at angle of [tex]45^{\circ}[/tex] to the intial direction
Suppose puck is travelling towards positive x axis
thus initial moment [tex]\vec{P_i}=0.166\times 19.5\hat{i}[/tex]
Final momentum [tex]\vec{P_f}=0.166\left ( 43.1cos45\hat{i}+43.1sin45\hat{j}\right )[/tex]
Impusle[tex]=P_f-P_i=5.06\hat{i}+5.06\hat{j}-3.237\hat{i}[/tex]
[tex]I=1.823\hat{i}+5.06\hat{j}[/tex]
Angle between initial velocity and force
[tex]tan\theta =\frac{5.06}{1.823}[/tex]
[tex]\theta =70.18^{\circ}[/tex] w.r.t x-axis
and Fdt=Impulse
[tex]dt=112 ms=112\times 10^{-3} s[/tex]
[tex]\vec{F}=16.339\hat{i}+45.17\hat{j}[/tex]
[tex]|F|=\sqrt{16.34^2+45.17^2}=48.03 N[/tex]
The average force is equal to the product of mass and acceleration. The magnitude of the average force that was exerted on the puck will be 48.03 N.
What is the law of conservation of momentum?
According to the law of conservation of momentum, the momentum of the body before the collision is always equal to the momentum of the body after the collision.
The momentum of the body is given by the product of the mass and velocity of the body.
According to the law of conservation of momentum
Momentum before collision =Momentum after collision
The given data in the problem is;
m is the mass of puck=166 gram
u is the initial velocity=19.5 m/s
v is the final velocity=43.1 m/s
The initial momentum of the body is;
[tex]\rm P_i = 0.166 \times 19.5 \vec i[/tex]
The final momentum of the body is;
[tex]\rm P_f= 0.166 \times (43.1 cos 45 \vec i + 43.1 sin 45 \vec j)[/tex]
The change in the momentum is;
[tex]\rm P_f-\rm P_i = 0.166 \times (43.1 cos 45 \vec i + 43.1 sin 45 \vec j)-0.166 \times 19.5 \vec i \\\\ \rm P= 506.1 \vec i +5.06 \vec j -3.2371 \vec i[/tex]
The rate of change of the momentum is the impulse;
[tex]\rm I = \triangle p[/tex]
From Newton's second law;
[tex]\rm I = F \triangle t[/tex]
[tex]\vec F = 16.339 \vec I +45.71 \vec j \\\\ \vec F = \sqrt{(16.34)^2+(45.147)^2} \\\\ \vec F = 48.03[/tex]
Hence the magnitude of the average force that was exerted on the puck will be 48.03 N.
To learn more about the law of conservation of momentum refer to;
https://brainly.com/question/1113396
