A 45 kg skater is standing still in front of a wall. By pushing against the wall she propels herself backward with a velocity of -1.0 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).
thank you
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, which states that force (F) is equal to mass (m) multiplied by acceleration (a). In this case, the acceleration can be determined using the equation:
a = (v - u) / t
where:
- v is the final velocity (-1.0 m/s)
- u is the initial velocity (0 m/s)
- t is the time the force is applied (0.80 s)
So, the acceleration is:
a = (-1.0 m/s - 0 m/s) / 0.80 s
a = -1.0 m/s / 0.80 s
a = -1.25 m/s²
Next, we can use the formula F = m * a to calculate the force exerted on the wall:
F = 45 kg * (-1.25 m/s²)
F = -56.25 N
The magnitude of the average force she exerts on the wall is 56.25 N, and the direction is opposite to her velocity, which means it is in the forward direction.
To find the magnitude and direction of the average force the skater exerts on the wall, we can apply 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 skater is initially standing still, so her initial velocity (v₁) is 0 m/s. After pushing against the wall, she propels herself backward with a final velocity (v₂) of -1.0 m/s. The change in velocity (Δv) can be calculated as:
Δv = v₂ - v₁
= -1.0 m/s - 0 m/s
= -1.0 m/s
Now, we can calculate the acceleration using the formula:
a = Δv / t
where t is the time interval during which the skater pushes against the wall. In this case, t is given as 0.80 s. So:
a = -1.0 m/s / 0.80 s
= -1.25 m/s²
Now, we can find the force using Newton's second law:
F = m * a
= 45 kg * -1.25 m/s²
= -56.25 N
The magnitude of the force is 56.25 N, and since the skater propels herself backward, the direction of the force is opposite to her motion, so the force is in the positive direction.
Therefore, the magnitude and direction of the average force the skater exerts on the wall are 56.25 N in the positive direction.
Impulse = changeinMomentum
force*time=mass*changeinvelocity
Now note: it is the wall which pushes her, so the wall force is in the direction of her motion. The force she exerts is opposite to the wall.