A crane lifts a package of mass 121 kg. If the power output of the crane is 101 Watts, at what speed can the package be lifted, in m/s?
Po = F*d/t = M*g * V = 101 W. = 101 J/s, 121*9.8 * V = 101, V = 0.085 m/s.
To find the speed at which the package can be lifted, we need to consider the work done by the crane. The work (W) is given by the formula:
W = Force × Distance
In this case, the force applied by the crane is equal to the weight of the package, which is the mass (m) of the package multiplied by the gravitational acceleration (g). The gravitational acceleration is approximately 9.8 m/s² on the surface of the Earth.
Force = m × g
Next, we need to calculate the distance traveled by the package in a given time interval. Since we are looking for the speed, let's assume the time interval is one second (t = 1 s). The distance (d) can be calculated using the formula:
d = speed × time
Finally, we need to relate power (P), work (W), and time (t) using the formula:
P = W / t
Now, we can put together all the information and solve for the speed:
Step 1: Calculate the force (F)
F = m × g
= 121 kg × 9.8 m/s²
= 1185.8 N
Step 2: Calculate the work (W)
W = F × d
= 1185.8 N × d
Step 3: Calculate the distance (d)
Since t = 1 s, we have d = speed × 1 s, which simplifies to d = speed.
Step 4: Relate power (P), work (W), and time (t)
P = W / t
= (1185.8 N × d) / 1 s
Step 5: Solve for the speed
101 Watts = (1185.8 N × d) / 1 s
To find the speed (d), rearrange the equation:
d = (101 Watts × 1 s) / 1185.8 N
Now substitute the given values:
d = (101 W × 1 s) / 1185.8 N
Simplifying:
d ≈ 0.085 m/s
Therefore, the package can be lifted at a speed of approximately 0.085 m/s.