Respuesta :
Answer:
[tex] W = W_A + W_B = 872.2 N + 602.462 N =1474.662 N[/tex]
Explanation:
For this case we can begin finding the weigth associated to the athlete like this:
[tex] w_A = m_a g = 89 kg * 9.8 m/s^2 = 872.2 N[/tex]
Now we can find the acceleration associated to the barbell using the following formula from kinematics:
[tex] y_f = y_i + v_i t + \frac{1}{2}a t^2[/tex]
We assume that the [tex] y_i =0[/tex] and the initial velocity is 0 so then we have:
[tex] y_f = \frac{1}{2}a t^2[/tex]
And we can find the acceleration since we have the height and the time like this:
[tex] a= \frac{2 y_f}{t^2}= \frac{2*0.5 m}{(2.2s)^2}= 0.207 m/s^2[/tex]
The mass of the barble would be:
[tex] m_B = \frac{590 N}{9.8 m/s^2}= 60.204 kg[/tex]
With this acceleration we can find the apparent weigth of the barbell like this:
[tex] W_B = m (g+a) = 60.204 Kg (9.8+0.207)m/s^2 = 602.462 N[/tex]
And finally the force exerted on the ground would be the sum of the two weigths:
[tex] W = W_A + W_B = 872.2 N + 602.462 N =1474.662 N[/tex]
The total force that his feet exert on the ground as he lifts the barbell is equal to 1,474.62 Newton.
Given the following data:
- Mass of athlete = 89 kg
- Weight of barbell = 590 N
- Distance = 0.5 m
- Time = 2.2 seconds
- Initial velocity = 0 m/s (since the athlete starts from rest).
We know that the acceleration due to gravity (g) of an object on planet Earth is equal to 9.8 [tex]m/s^2[/tex]
To find the total force that his feet exert on the ground as he lifts the barbell, we would apply Newton's laws:
First of all, we would determine the acceleration of the barbell by using the second equation of motion:
[tex]S = ut + \frac{1}{2} at^2\\\\0.50 = 0(t) + \frac{a}{2} \times 2.2^2\\\\0.50 = 2.42a\\\\a = \frac{0.5}{2.42}[/tex]
Acceleration = 0.207 [tex]m/s^2[/tex]
For the weight of athlete:
[tex]W_A = 89 \times 9.8\\\\W_A = 872.2 \;Newton[/tex]
For the mass of barbell:
[tex]590 = mass \times 9.8\\\\Mass = \frac{590}{9.8}[/tex]
Mass = 60.20 kg
Next, we would find the tension of the barbell:
[tex]T = m(a + g)\\\\T = 60.20(0.207 + 9.8)\\\\T = 60.20(10.007)[/tex]
Tension = 602.42 Newton
For the total force:
[tex]Total \;force = 602.42 + 872.2[/tex]
Total force = 1,474.62 Newton.
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