friction force does -200 J of work on a baseball player of mass 45.0 kg when she has stopped after sliding into second base. what was her initial velocity?
KE = 0.5M*V^2 = 200.
0.5*45*V^2 = 200,
V = ?
(1/2) m v^2 = Ke = work done to stop = 200
22.5 v^2 = 200
To find the initial velocity of the baseball player, we can use the work-energy principle. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.
The work done by the friction force can be calculated using the formula:
Work = force × distance × cos(θ)
In this case, the work done is given as -200 J, which means the work done by the friction force is negative, indicating that the friction force is in the opposite direction to the displacement. The distance is not provided, but it is not necessary to determine the initial velocity.
The change in kinetic energy can be calculated using the formula:
ΔKE = (1/2) × mass × (vf^2 - vi^2)
Since the player has stopped, the final velocity (vf) is 0 m/s.
We can equate the work done to the change in kinetic energy:
-200 J = (1/2) × 45.0 kg × (0^2 - vi^2)
Simplifying the equation, we get:
-200 J = -22.5 kg · vi^2
Divide both sides by -22.5 kg to isolate vi^2:
8.89 m^2/s^2 = vi^2
Taking the square root of both sides gives:
vi ≈ ±2.98 m/s
The initial velocity is approximately ±2.98 m/s. Since the direction is not specified, the player could be moving either towards or away from second base.