A helicopter lifts a 63 kg astronaut 10 m vertically from the ocean by means of a cable. The acceleration of the astronaut is g/10.

(a) How much work is done on the astronaut by the force from the helicopter?

Incorrect: Your answer is incorrect.
J

(b) How much work is done on the astronaut by her weight?

Correct: Your answer is correct.
J

(c)What is the kinetic energy?
J

(d) What is the speed of the astronaut just before she reaches the helicopter?

To solve this problem, we need to use the formulas for work, potential energy, and kinetic energy.

(a) To calculate the work done on the astronaut by the force from the helicopter, we can use the formula:

Work = Force * Distance

The force is equal to the weight of the astronaut, which is given by the formula:

Weight = mass * acceleration due to gravity

Weight = 63 kg * (9.8 m/s^2)

Now we can calculate the work done by the force from the helicopter:

Work = Weight * Distance

Work = (63 kg * 9.8 m/s^2) * 10 m

Work = 6174 J

So, the work done on the astronaut by the force from the helicopter is 6174 Joules.

(b) The work done on the astronaut by her weight is equal to the change in potential energy. The formula for potential energy is:

Potential Energy = mass * acceleration due to gravity * height

Potential Energy = 63 kg * 9.8 m/s^2 * 10 m

Potential Energy = 61740 J

So, the work done on the astronaut by her weight is 61740 Joules.

(c) The kinetic energy can be found using the formula:

Kinetic Energy = 1/2 * mass * velocity^2

Since the astronaut is lifted vertically, her initial velocity is 0. Therefore, the final kinetic energy is also 0. So, the kinetic energy is 0 Joules.

(d) The speed of the astronaut just before she reaches the helicopter can be found using the equation:

Kinetic Energy = 1/2 * mass * velocity^2

Since the kinetic energy is 0, we have:

0 = 1/2 * 63 kg * velocity^2

Solving for velocity:

0 = 31.5 kg * velocity^2

velocity^2 = 0

velocity = 0 m/s

So, the speed of the astronaut just before she reaches the helicopter is 0 m/s.

To find the answer to part (a), we need to calculate the work done by the force from the helicopter.

Work is defined as the product of force and displacement. In this case, the work done on the astronaut is equal to the force exerted by the helicopter multiplied by the distance the astronaut is lifted vertically.

The force exerted by the helicopter can be found using Newton's second law: F = m * a, where m is the mass of the astronaut and a is the acceleration experienced by the astronaut. Given that the acceleration is g/10 and the mass is 63 kg, we can calculate the force:

F = m * a = 63 kg * (g/10)

Now, we can calculate the work done by the force of the helicopter:

Work = F * d = (63 kg * (g/10)) * 10 m

To find the answer to part (b), we need to calculate the work done on the astronaut by her weight.

The work done by her weight is equal to the weight multiplied by the distance she is lifted. The weight of the astronaut can be found using the formula: Weight = m * g, where m is the mass of the astronaut and g is the acceleration due to gravity.

Given that the mass is 63 kg, we can calculate the weight:

Weight = m * g = 63 kg * g

Now, we can calculate the work done by her weight:

Work = Weight * d = (63 kg * g) * 10 m

For part (c), we need to find the kinetic energy of the astronaut.

The kinetic energy is given by the formula: KE = 1/2 * m * v^2, where m is the mass of the astronaut and v is the velocity.

The velocity just before the astronaut reaches the helicopter can be found using the kinematic equation:

v^2 = u^2 + 2 * a * d

Where u is the initial velocity (which is 0 in this case, as the astronaut starts from rest) and a is the acceleration experienced by the astronaut. Given that the acceleration is g/10 and the distance lifted is 10 m, we can calculate the velocity:

v^2 = 0 + 2 * (g/10) * 10 m

Finally, we can find the kinetic energy using the formula:

KE = 1/2 * m * v^2 = 1/2 * 63 kg * v^2

Let's calculate the values to find the answers.

a. Work = F * d = m*g/10 * d

Work = 63*(9.8/10) * 10 = 617.4 Joules.

b. Work=m*g * d = 63*9.8 * 10 = 6174 J.