A sled with mass 20 kg is given a shove up a frictionless incline which makes an angle of 28 degrees with the horizontal. eventually the sled comes to rest at height of 1.35 m above where it started. a)calculate its initial speed. b)find the work done by the weight of the sled.

Vf^2 = = Vo^2 + 2gd = 0,

a. Vo^2 - 2*9.8 * 1.35 = 0,
Vo^2 - 26.46 = 0,
Vo^2 = 26.46,
Vo = 5.14m/s.

b. Fs = mg = 20kg * 9.8N/kg = 196N. =
Force of the sled.

196 @ 28deg.

Fp=196sin28 = 92N. = Force of the sled acting parallel to plane downward.

d=1.35m / sin28 = 2.88m = The distance traveled up the plane.

W = Fp*d = 92 * 2.88 = 265 Joules.

To solve this problem, we can use principles of energy conservation. The total mechanical energy of the sled, which is the sum of its kinetic energy and its potential energy, remains constant throughout the motion.

a) To calculate the initial speed of the sled, we can equate its initial mechanical energy to the potential energy at its final position.

The potential energy of the sled at the top of the incline is given by:
PE = m * g * h

Where m is the mass of the sled (20 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the vertical height above the starting position (1.35 m).

So, the potential energy at the top of the incline is:
PE = (20 kg) * (9.8 m/s^2) * (1.35 m) = 264.6 Joules

The initial mechanical energy of the sled is the sum of its initial kinetic energy (KE) and its initial potential energy (PE). Since the sled is initially at rest, its initial kinetic energy is zero.

Therefore, the initial mechanical energy of the sled is equal to its initial potential energy:
KE + PE = 264.6 Joules

Since the initial kinetic energy is zero, the initial mechanical energy is equal to the initial potential energy. Thus,

KE = 264.6 Joules

To find the initial speed (v), we can use the equation for kinetic energy:

KE = 1/2 * m * v^2

Rearranging the equation, we have:
v = sqrt((2 * KE) / m)

Substituting the values, we get:
v = sqrt((2 * 264.6) / 20) = 6.47 m/s

Therefore, the initial speed of the sled is 6.47 m/s.

b) The work done by the weight of the sled can be calculated using the equation:

Work = force * distance * cos(theta)

Where force is the weight of the sled (mg), distance is the horizontal distance covered, and theta is the angle between the force and displacement vectors.

The work done by the weight of the sled is equal to the change in potential energy, which is given by:
Work = m * g * (h_final - h_initial)

Substituting the values, we have:
Work = (20 kg) * (9.8 m/s^2) * (1.35 m - 0 m) = 264.6 Joules

Therefore, the work done by the weight of the sled is 264.6 Joules.