Question:

An object of mass 2 kg is lifted vertically a distance of 5 meters in 2 seconds. Calculate the power delivered to the object during this time. Assume the acceleration due to gravity is 9.8 m/s².

Answer:

Given information:

• Mass of the object, m = 2 kg
• Distance traveled vertically, d = 5 m
• Time taken, t = 2 s
• Acceleration due to gravity, g = 9.8 m/s²

To find the power delivered to the object, we can use the formula:

Power (P) = Work (W) / Time (t)

To find the work done, we need to find the force (F) applied on the object. Since the object is lifted vertically against gravity, the force applied will be equal to the weight of the object, which is given by:

Weight (w) = mass (m) * acceleration due to gravity (g)

Substituting the given values:

w = 2 kg * 9.8 m/s²

w = 19.6 N

Now, we can find the work done using the equation:

Work (W) = Force (F) * Distance (d)

Substituting the values:

W = 19.6 N * 5 m

W = 98 J

Finally, we can find the power delivered using the equation:

P = W / t

Substituting the values:

P = 98 J / 2 s

P = 49 W

Therefore, the power delivered to the object during the lift is 49 Watts.

Explanation:

In this question, we are given the mass of an object, the vertical distance it is lifted, and the time taken for the lift. We need to calculate the power delivered to the object.

Power is the rate at which work is done or energy is transferred. The formula for power is given by:

Power (P) = Work (W) / Time (t)

To find the work done during the lift, we first need to find the force applied on the object. Since the object is lifted vertically against gravity, the force applied will be equal to the weight of the object. The weight (w) is given by the formula:

Weight (w) = mass (m) * acceleration due to gravity (g)

Substituting the given values of mass and acceleration due to gravity, we calculate the weight as 19.6 N.

The work done is obtained by multiplying the force applied with the distance traveled. The formula for work is given by:

Work (W) = Force (F) * Distance (d)

Substituting the values, we calculate the work done as 98 J.

Finally, we substitute the values of work and time into the power formula to find the power delivered during the lift. We calculate the power to be 49 Watts.

Therefore, the power delivered to the object during the lift is 49 Watts.