A girl(60 kg) is sliding in the snow towards a cliff that is only 15 meters away. She is moving 6 m/s. She digs her fingers into the snow to try and save herself. How much force do her fingers need to provide if she is going to successfully stop in time?
To calculate the force required for the girl to stop in time, we can use the equation for change in momentum. The change in momentum is equal to the force applied multiplied by the time taken. Assuming that the girl applies the force over a short period of time and comes to a stop, the change in momentum would be equal to her initial momentum.
The initial momentum of the girl can be calculated using the mass and velocity. The momentum (p) is given by the equation p = mass × velocity.
Given:
Mass (m) = 60 kg
Velocity (v) = 6 m/s
Initial momentum (p) = m × v = 60 kg × 6 m/s = 360 kg⋅m/s
Since the girl stops, the change in momentum (Δp) is equal to the initial momentum.
Δp = 360 kg⋅m/s
The change in momentum can also be represented as the force (F) applied multiplied by the time (t) taken to stop. So, we have F × t = 360 kg⋅m/s.
However, we don't have the given value for time (t) in this case. To determine the force required, we need the time taken to stop. The time can be calculated using the distance (d) and velocity (v), using the equation t = d/v.
Given:
Distance (d) = 15 m
Velocity (v) = 6 m/s
Time (t) = d/v = 15 m / 6 m/s ≈ 2.5 seconds
Substituting the time value into the equation F × t = 360 kg⋅m/s, we have:
F × 2.5 seconds = 360 kg⋅m/s
Solving for force (F):
F = 360 kg⋅m/s ÷ 2.5 seconds
F ≈ 144 Newtons
Therefore, to successfully stop in time, the girl's fingers need to provide approximately 144 Newtons of force.