need help quick:
Magen's mass is 25 kg. She climbs the 4.5-m ladder of a slide, and reaches a velocity of 3.0 m/s at the bottom of the slide. How much work was done by friction on Magen?
Subtract her kinetic energy at the bottom of the slide from her potential energy at the top.
M g H - (M/2) V^2 = 1102.5 - 112.5 = _____ J
The difference is the work lost to friction. (Work done BY friction is considered negative, so they may want you to put a minus sign before the answer)
To calculate the work done by friction on Magen, we need to use the work-energy principle. The work done by a force is defined as the product of the force and the distance over which it acts.
In this case, the frictional force acts on Magen as she slides down the ladder. We can calculate the work done by friction using the given information.
First, we need to find the gravitational potential energy (GPE) converted to kinetic energy (KE) as Magen slides down the ladder. The GPE is given by the equation:
GPE = mgh
where m is the mass, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height Magen climbs.
Since Magen climbs the 4.5-m ladder, the height h = 4.5 m. Plugging in the values:
GPE = (25 kg) * (9.8 m/s²) * (4.5 m) = 1102.5 Joules
Next, using the conservation of energy, we know that the GPE is converted entirely into kinetic energy at the bottom of the slide. The kinetic energy is given by the equation:
KE = 0.5 * mv²
where m is the mass and v is the velocity.
Plugging in the values:
KE = 0.5 * (25 kg) * (3.0 m/s)² = 112.5 Joules
Lastly, to find the work done by friction, we need to subtract the kinetic energy from the gravitational potential energy:
Work by friction = GPE - KE = 1102.5 Joules - 112.5 Joules = 990 Joules
Therefore, the work done by friction on Magen is 990 Joules.