A young girl (m= 30 kg) rides a skateboard (m= 3.2 kg) at a speed of 4.2 m/s.
(a)
How much work does
the girl have to do to bring herself to a stop?
(b)
How far does she travel if it takes 6.0 s to stop?
(c)
What
is the magnitude of the stopping force?
So I know W=Fd but I am having trouble trying to figure out how her stopping plays into this whole problem. Does that mean her final velocity is 0? I am super confused.
To solve this problem, we can break it down into several steps.
(a) To find the work done by the girl to bring herself to a stop, we first need to determine the initial and final kinetic energies of the system. The initial kinetic energy is given by:
KE_i = (1/2) * m_girl * v_initial^2
where m_girl is the mass of the girl (30 kg) and v_initial is the initial velocity (4.2 m/s). Plugging in the values:
KE_i = (1/2) * 30 kg * (4.2 m/s)^2 = 264.6 J
Since the final velocity is zero, the final kinetic energy is also zero:
KE_f = 0 J
The work done by the girl is equal to the change in kinetic energy of the system:
Work = KE_f - KE_i = 0 J - 264.6 J = -264.6 J
Note that the negative sign indicates that work is done against the motion, resulting in a decrease in kinetic energy.
(b) To find the distance traveled by the girl during the time it takes to stop (6.0 s), we can use the equation for deceleration:
a = (v_final - v_initial) / t
Since the final velocity is zero, the equation becomes:
a = -v_initial / t
Substituting the given values:
a = -(4.2 m/s) / (6.0 s) = -0.7 m/s^2
Now, we can use the equation of motion for constant acceleration:
d = v_initial * t + (1/2) * a * t^2
Plugging in the values:
d = (4.2 m/s) * (6.0 s) + (1/2) * (-0.7 m/s^2) * (6.0 s)^2 = 12.6 m
Therefore, the girl travels a distance of 12.6 meters.
(c) To find the magnitude of the stopping force, we can use Newton's second law of motion:
F = m_girl * a
Substituting the mass of the girl (30 kg) and the deceleration (-0.7 m/s^2) found earlier:
F = (30 kg) * (-0.7 m/s^2) = -21 N
The negative sign indicates that the force is in the opposite direction to the initial motion, in this case, the stopping force exerted by the girl against the skateboard.
I hope this explanation helps in solving the problem! Let me know if you have any further questions.