Physics, 29.06.2019 08:30 rosezgomez97

Achild and sled with a combined mass of 50.0 kg slide down a frictionless hill that is 7.34 m high. if the sled starts from rest, what is the mechanical energy of the system, and what is the sled's speed at the bottom of the hill?

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Answer from: gigipalacio32

The mechanical energy of the system is 3596.6 J and the speed of sled at the bottom of hill is 11.99 m/s.

Given data:

The mass of child-sled system is, m = 50.0 kg.

The height of system on the hill is, h = 7.34 m.

The mechanical energy of the system at any point is the combination of kinetic energy as well as potential energy of the system at that point.

Mechanical Energy = Kinetic Energy + Potential Energy

$ME =\dfrac{1}{2}mv^{2} +mgh$

Here, v is the speed of system, since child and sled were at rest initially. Then, v = 0 m/s.

Solving as,

$ME =\dfrac{1}{2} \times 50 \times 0^{2} +(50 \times 9.8 \times 7.34)\\\\ME = 3596.6 \;\rm J$

And at the bottom of the hill, the potential energy of the system is zero. Which means,

Mechanical Energy = Kinetic Energy + Potential Energy

Mechanical Energy = Kinetic Energy + 0

$ME = \dfrac{1}{2}mv'^{2}$

Here, v' is the speed of sled at bottom of hill.

Solving as,

$3596.6 = \dfrac{1}{2} \times 50 \times v'^{2}\\\\v' = 11.99 \;\rm m/s$

Thus, we can conclude that the mechanical energy of the system is 3596.6 J and the speed of sled at the bottom of hill is 11.99 m/s.

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Answer from: ralphmillerrr

1. Mechanical energy of the system: 3597 J

The mechanical energy of the system is equal to the sum of the kinetic energy (K) and the gravitational potential energy (U):

E=K+U

However, the sled starts from rest, so the initial kinetic energy is zero: K=0. Therefore, at the top of the hill all the mechanical energy is just potential energy, given by:

U=mgh

where m=50.0 kg is the mass, g=9.8 m/s^2 the acceleration due to gravity and h=7.34 m is the height. Substituting,

E=U=(50.0 kg)(9.8 m/s^2)(7.34 m)=3597 J

2. Sleed's speed at the bottom of the hill: 12.0 m/s

At the bottom of the hill, h=0, so the potential energy has become zero: U=0. However, the mechanical energy must be conserved, so all this energy has been converted into kinetic energy:

E=K=3597 J

The formula for the kinetic energy is:

$K=\frac{1}{2}mv^2$

where m=50.0 kg is the mass and v the speed of the sled at the bottom of the hill. Re-arranging the equation, we find v:

$v=\sqrt{\frac{2K}{m}}=\sqrt{\frac{2(3597 J)}{50.0 kg}}=12.0 m/s$

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Achild and sled with a combined mass of 50.0 kg slide down a frictionless hill that is 7.34 m high....

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