A 40-kg skater is standing still in front of a wall. By pushing against the wall she propels herself backward with a velocity of -1.8 m/s. Her hands are in contact with the wall for 0.80 s. Ignore friction and wind resistance. Find the magnitude and direction of 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).
Force = ((mass)(velocity))/Time
To find the magnitude and direction of the average force the skater exerts on the wall, we can use Newton's second law of motion, F = m * a, where F is the force, m is the mass, and a is the acceleration.
In this case, the initial velocity of the skater is 0 m/s (standing still) and the final velocity is -1.8 m/s (moving backward). The change in velocity is given by:
Δv = -1.8 m/s - 0 m/s = -1.8 m/s
The time taken for this change in velocity is 0.80 s.
To calculate acceleration, we can use the formula:
a = Δv / t
Substituting the values, we get:
a = -1.8 m/s / 0.80 s = -2.25 m/s^2
Since the acceleration is negative, it means the skater is decelerating or slowing down.
Now, we can use Newton's second law to find the magnitude of the force:
F = m * a
Substituting the values, we get:
F = 40 kg * -2.25 m/s^2 = -90 N
The negative sign represents the direction opposite to the motion of the skater. So, the magnitude of the average force the skater exerts on the wall is 90 N, and it is in the forward direction.
To solve this problem, we can use Newton's second law of motion, which states that the force exerted on an object is equal to the mass of the object multiplied by its acceleration.
In this case, the skater exerts a force on the wall, causing herself to move backward. Since the skater is initially at rest and ends up with a velocity of -1.8 m/s, she experiences an acceleration during the time she pushes against the wall.
We can calculate the acceleration using the kinematic equation:
v = u + at
Where:
v = final velocity (-1.8 m/s)
u = initial velocity (0 m/s, since the skater is initially at rest)
a = acceleration
t = time (0.80 s)
Rearranging the equation to solve for acceleration (a), we have:
a = (v - u) / t
Substituting the given values, we find:
a = (-1.8 m/s - 0 m/s) / 0.80 s
a = -2.25 m/s^2
Now that we have the acceleration, we can use Newton's second law to determine the magnitude of the force exerted on the wall:
F = m * a
Substituting the given mass of the skater (40 kg) and the calculated acceleration (-2.25 m/s^2), we have:
F = 40 kg * (-2.25 m/s^2)
F = -90 N
Since the force exerted on the skater is in the opposite direction to her motion, the direction of the average force she exerts on the wall is forward (opposite to the skater's motion). The magnitude of this force is 90 N.
avgforce*time= mass*changevelocity
This is the force the wall exerts on her, reverse the direction for her force.