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 -1.82 m/s. Her hands are in contact with the wall for 1.16 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.

Question

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 -1.82 m/s. Her hands are in contact with the wall for 1.16 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.

Answer 1

force on her yields negative velocity so by third law her force on the wall is positive.

Change in Ke = (1/2)(40.2)(-1.82)^2 = work done
so
F * distance = Change in Ke
distance = average speed *time = (-1.82/2) * 1.16
so
F = - (20.1)(1.82^2) /[ 1.82 * 0.58 ]
= - (20.1)(1.82) / 0.58

Answer 2

V = Vo + a*t = -1.82.

0 + a*1.16 = -1.82,
a = -1.57 m/s^2.

F = M*a = 40.2 * (-1.57) =

Answer 3

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.

Here's how we can find the force:

Step 1: Identify the given values:
Mass of the skater (m) = 40.2 kg
Initial velocity of the skater (u) = 0 m/s (since she is at rest)
Final velocity of the skater (v) = -1.82 m/s (negative because she is moving backward)
Time (t) = 1.16 s

Step 2: Calculate the acceleration:
We can find the acceleration using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Rearranging the equation, we have a = (v - u) / t.
Substituting the values, we get a = (-1.82 - 0) / 1.16 = -1.57 m/s^2 (negative because the skater is slowing down).

Step 3: Calculate the force:
Now, we can use Newton's second law of motion, F = ma, where F is the force, m is the mass, and a is the acceleration.
Substituting the values, we get F = 40.2 kg * -1.57 m/s^2 = -63.114 N (rounded to three significant figures).
Since the force is in the opposite direction to the skater's motion, we indicate it with a negative sign.
Therefore, the average force the skater exerts on the wall is approximately -63.114 N.