A loaded ore car has a mass of 880 kg and rolls on rails with negligible friction. It starts from rest and is pulled up a mine shaft by a cable connected to a winch. The shaft is inclined at 28.0° above the horizontal. The car accelerates uniformly to a speed of 2.20 m/s in 11.5 s and then continues at constant speed.
What maximum power must the winch motor provide?
Whoa!
I left out gravity
Total force = mass * acceleration
F - 4049 = m a = 168 N
F = 4049+168 = 4217 N
power = 4217*2.2 = 9277 Watts
Gravity Force component down track = 880 * 9.8 * sin 28
= 4049 Newtons
acceleration =a = 2.20 / 11.5 = .191 m/s^2
Force = m a = 880 * .191 = 168 Newtons
max Power = force * max velocity = 168*11.5 max = 1933 Watts
I confused the time with the speed in the last line
max Power = force * max velocity = 168*2.2 max = 370 Watts
its not correct...because that is what i did too
A loaded ore car has a mass of 880 kg and rolls on rails with negligible friction. It starts from rest and is pulled up a mine shaft by a cable connected to a winch. The shaft is inclined at 28.0° above the horizontal. The car accelerates uniformly to a speed of 2.20 m/s in 11.5 s and then continues at constant speed
What maximum power must the winch motor provide?
To calculate the maximum power that the winch motor must provide, we need to use the equation for power:
Power = Force x Velocity
First, let's find the force acting on the loaded ore car. We can use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration:
Force = Mass x Acceleration
The acceleration of the car can be calculated using the given information that it starts from rest and reaches a speed of 2.20 m/s in 11.5 s. We can use the formula of motion:
v = u + at
where:
v = final velocity (2.20 m/s)
u = initial velocity (0 m/s)
a = acceleration (unknown)
t = time (11.5 s)
Rearranging the formula, we get:
a = (v - u) / t
Substituting the values, we find:
a = (2.20 m/s - 0 m/s) / 11.5 s
a = 2.20 m/s / 11.5 s
a = 0.1913 m/s² (approximately)
Now, we can calculate the force acting on the car:
Force = Mass x Acceleration
Force = 880 kg x 0.1913 m/s²
Force = 168.424 N (approximately)
Finally, we can calculate the maximum power required by the winch motor:
Power = Force x Velocity
Power = 168.424 N x 2.20 m/s
Power = 370.5336 W (approximately)
Therefore, the winch motor must provide a maximum power of approximately 370.5336 Watts.