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Can anyone please help?
The ski slopes at Bluebird Mountain make use of tow ropes to transport snowboarders and skiers to the summit of the hill. One of the tow ropes is powered by a 22-kW motor which pulls skiers along an icy incline of 14° at a constant speed. Suppose that 18 skiers with an average mass of 48 kg hold onto the rope and suppose that the motor operates at full power.
a. Determine the cumulative weight of all these skiers.
b. Determine the force required to pull this amount of weight up a 14° incline at a constant speed.
c. Determine the speed at which the skiers will ascend the hill.
2 Answers
- electron1Lv 76 years ago
Weight = 18 * 48 * 9.8 = 8467.2 N
Since the skiers are moving at a constant speed, the net force is 0 N. This means the tension in the rope is equal to the component of their weight that is parallel to the slope.
Force parallel = m * g * sin 14 = 8467.2 * sin 14
This is approximately 2,048.4 N.
Let’s convert the power to watts.
P = 22,000 watts
Power = Work ÷ time
Work = Force * distance
Velocity = distance ÷ time
Power = Force * velocity
Let’s use the force and the power to determine the velocity.
22,000 = 8,467.2 * sin 14 * v
v = 22,000 ÷ (8,467.2 * sin 14)
The velocity is approximately 10.74 m/s.
