A 53.8-kg skater is standing at rest in front of a wall. By pushing against the wall she propels herself backward with a velocity of -1.33 m/s. Her hands are in contact with the wall for 0.960 s. Ignore friction and wind resistance. Find the average force she exerts on the wall (which has the same magnitude, but opposite direction, as the force that the wall applies to her). Note that this force has direction, which you should indicate with the sign of your answer.
V = Vo + a*t.
-1.33 = 0 + a*0.96,
a = -1.33/0.96 = -1.39 m/s^2.
F = M*a = 53.8 * (-1.39) = -74.5 N.
To find the average force the skater exerts on the wall, we can use Newton's second law of motion, which states that force (F) is equal to the rate of change of momentum (mv):
F = Δp / Δt
Where:
F is the force applied
Δp is the change in momentum
Δt is the time interval
In this case, the skater initially stands at rest, so her initial momentum (p_initial) is zero. After pushing off the wall, her final momentum (p_final) can be calculated as:
p_final = m * v_final
Where:
m is the mass of the skater (53.8 kg)
v_final is the final velocity of the skater (-1.33 m/s)
p_final = 53.8 kg * (-1.33 m/s) = -71.554 kg·m/s
Now, we can calculate the change in momentum (Δp) as the difference between the final and initial momentum:
Δp = p_final - p_initial
Δp = -71.554 kg·m/s - 0 kg·m/s
Δp = -71.554 kg·m/s
The time interval (Δt) during which the skater applies force to the wall is given as 0.960 s.
Finally, we can substitute the values into the formula to find the average force:
F = Δp / Δt
F = (-71.554 kg·m/s) / (0.960 s)
F ≈ -74.51 N
Therefore, the average force the skater exerts on the wall is approximately -74.51 Newtons, with a direction opposite to the skater's motion.
To find the average force the skater exerts on the wall, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration.
In this case, the skater's mass is given as 53.8 kg and her velocity change is from 0 m/s to -1.33 m/s (since the final velocity is in the opposite direction). So, her acceleration can be calculated as:
acceleration = (final velocity - initial velocity) / time
acceleration = (-1.33 m/s - 0 m/s) / 0.960 s
acceleration = -1.33 m/s / 0.960 s
acceleration ≈ -1.39 m/s²
Now, we can calculate the average force she exerts on the wall using the equation:
force = mass * acceleration
force = 53.8 kg * (-1.39 m/s²)
force ≈ -74.682 N
Therefore, the average force she exerts on the wall is approximately -74.682 N. The negative sign indicates that the force is in the opposite direction to the skater's motion.