An athlete whose mass is 94.0 is performing weight-lifting exercises. Starting from the rest position, he lifts, with constant acceleration, a barbell that weighs 600 . He lifts the barbell a distance of 0.50 in a time of 2.2 .
Part A
Use Newton's laws to find the total force that his feet exert on the ground as he lifts the barbell.
Express your answer using two significant figures.
forcetotal=(hismass+barbellmass)g+barbellmass*acceleration
what is barbell acceleration: changevelocity/time=2*distance/time
To find the total force that the athlete's feet exert on the ground, we need to consider the forces acting on the athlete during the weight-lifting exercise.
According to Newton's laws of motion, the net force acting on an object is equal to its mass multiplied by its acceleration (F = m * a).
In this case, the mass of the athlete is given as 94.0 kg.
To find the acceleration of the athlete, we can use the equations of motion. The distance lifted by the athlete is given as 0.50 m, and the time taken to lift the barbell is given as 2.2 s. The equation that relates distance, time, initial velocity, final velocity, and acceleration is:
\[s = v_0t + \frac{1}{2}at^2\]
Since the athlete starts from rest (initial velocity = 0), the equation simplifies to:
\[s = \frac{1}{2}at^2\]
Rearranging the equation to solve for acceleration, we get:
\[a = \frac{2s}{t^2}\]
Plugging in the given values, we have:
\[a = \frac{2(0.50)}{(2.2)^2}\]
Calculating the acceleration gives us:
\[a = 0.411 \, \text{m/s}^2\]
Now, we can find the total force by using Newton's second law:
\[F = m \cdot a\]
Plugging in the values, we have:
\[F = (94.0)(0.411)\]
Calculating this gives us:
\[F = 38.6 \, \text{N}\]
Therefore, the total force that the athlete's feet exert on the ground as he lifts the barbell is approximately 38.6 N.