How long will it take a 480 N motor to lift a 335 kg piano to a sixth-story window 15.0 m above?

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480 N is not a power specification. It is a force specification. Newtons (N) measure force.

You need a specification of motor power (such as horsepower or Watts) to answer this question. Any motor can provide an arbitrary force by using levers or hydraulic pistons for mechanical advantage.

Show that 480 W of power is expended by a weightlifter when lifting a 60-kg barbell a vertical distance of 1.2 m in a time interval of 1.5 s.

5m

To find the time it takes for the motor to lift the piano to the sixth-story window, we need to use the equation for work. The work done on an object is equal to the force applied on the object multiplied by the distance the object moves in the direction of the force.

Let's break down the problem and use the following formulas:

1. Work (W) = Force (F) x Distance (d)
2. Force (F) = Mass (m) x acceleration due to gravity (g)
3. Distance (d) = height of the window (h)

First, we need to calculate the force applied by the motor. The force can be determined using the formula F = mg, where m is the mass of the piano and g is the acceleration due to gravity (approximately 9.8 m/s^2).

Given:
Mass of the piano (m) = 335 kg
Acceleration due to gravity (g) = 9.8 m/s^2

Calculating the force applied by the motor:
F = mg
F = 335 kg x 9.8 m/s^2
F ≈ 3283 N

Now that we have the force (F) applied by the motor, we can calculate the work done (W) by multiplying it with the distance (d) the piano needs to be lifted, which is the height of the window.

Given:
Distance (d) = 15.0 m

Calculating the work done by the motor:
W = F x d
W = 3283 N x 15.0 m
W ≈ 49,245 J

The work done on the piano is approximately 49,245 joules.

To find the time it takes to lift the piano, we also need the power (P) of the motor. Power is defined as the rate at which work is done or energy is transferred.

Given:
Power (P) = 480 N
Time (t) = ? (to be determined)

Power is calculated using the formula:
Power (P) = Work (W) / Time (t)

Rearranging the formula to solve for time:
Time (t) = Work (W) / Power (P)

Substituting the known values:
Time (t) = 49,245 J / 480 N
Time (t) ≈ 102.178 sec

Therefore, it will take approximately 102.178 seconds for the 480 N motor to lift the 335 kg piano to the sixth-story window that is 15.0 m above.