A 2.0-kg wooden block slides down an inclined plane 1.0 m high and 3.0 m long. The block starts from rest at the top of the plane. The coefficient of kinetic friction between the block and plane is 0.35. What is the speed of the block when it reaches the bottom?

Sin¤= 1/3

¤=19.47'

Fnet= Fg// - Ff
Fnet= mg.sin¤ -Ff
=2(9.8)sin19.47-0.35
Fnet= 6.183N

a= Fnet/m
a= 6.183/2
a=3.091m/s^2

(Vf^2)=(Vi^2) +2as
Vf^2= (0)+2(3.091)(3)
Vf^2= 18.546
Vf= 4.31m/s downward.

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a skier starts from rest and slide 9 m down a slope in 3 s. at what time, after starting, will the skier acquire a velocity of 24m/s? assume constant acceleration.

how can you solve it using work power and energy?

To find the speed of the block when it reaches the bottom of the inclined plane, we can use the principles of conservation of energy and Newton's laws of motion.

1. Find the gravitational potential energy at the top:
The block has a mass of 2.0 kg and the height of the inclined plane is 1.0 m. The gravitational potential energy at the top is given by the formula:
Gravitational Potential Energy (PE) = m * g * h,
where m is the mass, g is the acceleration due to gravity (9.8 m/s^2), and h is the height.
PE = 2.0 kg * 9.8 m/s^2 * 1.0 m
PE = 19.6 Joules

2. Find the work done by friction:
The coefficient of kinetic friction between the block and the plane is 0.35. The work done by friction is given by the formula:
Work (W) = friction force * distance,
where the friction force is the product of the coefficient of kinetic friction and the normal force (which is the weight of the block perpendicular to the plane).
The normal force can be calculated using the formula:
Normal force (N) = m * g * cos(theta),
where theta is the angle of the incline (which can be found using the height and length of the inclined plane).
N = 2.0 kg * 9.8 m/s^2 * cos(theta)
N = 19.6 N * cos(theta)

The friction force (Ffriction) is the product of the normal force and the coefficient of kinetic friction:
Ffriction = 0.35 * 19.6 N * cos(theta)

The distance traveled along the incline is 3.0 m.
The work done by friction is then:
W = Ffriction * d
W = 0.35 * 19.6 N * cos(theta) * 3.0 m

3. Calculate the work done against gravity:
The work done against gravity is equal to the change in potential energy:
W = ∆PE
W = PE at the top - PE at the bottom
W = 19.6 J - 0 J
W = 19.6 J

4. Calculate the net work done:
The net work done on the block is the sum of the work done by friction and the work done against gravity:
Net Work = W_friction + W_gravity
Net Work = 0.35 * 19.6 N * cos(theta) * 3.0 m + 19.6 J

5. Calculate the kinematic work-energy equation to solve for the final velocity:
The net work done on an object is equal to its change in kinetic energy.
Net Work = ∆KE = ∆(1/2 * mass * velocity^2)
Therefore, ∆KE = (1/2) * mass * (final velocity^2 - initial velocity^2)
We know that the block starts from rest, so the initial velocity is 0 and the equation simplifies to:
Net Work = (1/2) * mass * final velocity^2
Solving for the final velocity:
final velocity^2 = (Net Work * 2) / mass
final velocity^2 = [(0.35 * 19.6 N * cos(theta) * 3.0 m + 19.6 J) * 2] / 2.0 kg
final velocity^2 = (0.35 * 19.6 N * cos(theta) * 3.0 m + 19.6 J) / kg
final velocity = sqrt{(0.35 * 19.6 N * cos(theta) * 3.0 m + 19.6 J) / kg}

Plug in the value for cos(theta) based on the given dimensions of the inclined plane, and calculate the final velocity.