A 40.2-kg skater is standing at rest in front of a wall. By pushing against the wall she propels herself backward with a velocity of -1.84 m/s. Her hands are in contact with the wall for 1.17 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.
F (1.17) = 40.2(-1.84) ON her
so
she pushes the wall (Newton's third law) equal and opposite
(40.2)(+1.84)/1.17
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 the rate of change of momentum. The momentum of an object is given by the product of its mass and velocity.
The skater's initial momentum, before pushing off the wall, can be calculated as follows:
Initial momentum = mass × initial velocity = 40.2 kg × 0 m/s = 0 kg∙m/s
After pushing off the wall, the skater's final momentum can be calculated as follows:
Final momentum = mass × final velocity = 40.2 kg × (-1.84 m/s) = -73.968 kg∙m/s
The change in momentum can be calculated by subtracting the initial momentum from the final momentum:
Change in momentum = Final momentum - Initial momentum = -73.968 kg∙m/s - 0 kg∙m/s = -73.968 kg∙m/s
Now, we can calculate the average force using the formula:
Average force = Change in momentum / Time
Plugging in the given values:
Average force = -73.968 kg∙m/s / 1.17 s = -63.158 kg∙m/s²
Since force is a vector quantity, the negative sign indicates the opposite direction of the force exerted on the wall. Therefore, the average force the skater exerts on the wall is approximately 63.158 N in the opposite direction to her motion.