A 51.2-kg skater is standing at rest in front of a wall. By pushing against the wall she propels herself backward with a velocity of -1.99 m/s. Her hands are in contact with the wall for 1.20 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.
acceleration = (1.99 m/s) / 1.20 s
force = mass * acceleration ... one of Newton's laws
because her resultant velocity is negative
... the force she exerts on the wall is positive
To find the average force that the skater exerts on the wall, we can use Newton's second law of motion, which states:
Force = mass x acceleration
In this case, the skater is pushing against the wall, so the force she exerts on the wall is equal in magnitude and opposite in direction to the force that the wall applies to her.
First, let's find the skater's acceleration. We can use the equation:
Acceleration = (final velocity - initial velocity) / time
Given:
- Skater's mass (m) = 51.2 kg
- Initial velocity (u) = 0 m/s (at rest)
- Final velocity (v) = -1.99 m/s (negative sign indicates the opposite direction)
- Time (t) = 1.20 s
Substituting the values into the equation, we have:
Acceleration = (-1.99 m/s - 0 m/s) / 1.20 s
Acceleration = -1.99 m/s / 1.20 s
Acceleration = -1.66 m/s²
Now, we can calculate the force using the equation:
Force = mass x acceleration
Force = 51.2 kg x (-1.66 m/s²)
Force = -84.352 N
The negative sign in the force indicates that the force is in the opposite direction to the skater's motion. Therefore, the skater exerts an average force of -84.352 N on the wall.