A skier of mass 74.6 kg is pulled up a slope
by a motor-driven cable.
How much work is required to pull the skier
63.3 m up a 39.0◦
slope (assumed to be frictionless)
at a constant speed of 2.0 m/s? The
acceleration of gravity is 9.81 m/s
2
.
Answer in units of J
M*g = 74.6kg * 9.8N/kg = 731.1 N. = Wt.
of the skier.
Fp = 731.1*sin39.0 = 460.1 N. = Force
parallel to the incline.
Work = Fp*d = 460.1 * 63.3 = 29,124 J.
The work done to pull the skier up the slope can be calculated using the formula:
Work = Force × Distance × cos(theta)
Where:
Force = mass × acceleration due to gravity = 74.6 kg × 9.81 m/s^2
Distance = 63.3 m
theta = 39.0° (converted to radians by multiplying by pi/180)
Let's calculate the work:
Force = 74.6 kg × 9.81 m/s^2 = 731.8266 N
theta = 39.0° × (pi/180) ≈ 0.6807 radians
Work = 731.8266 N × 63.3 m × cos(0.6807)
Using a calculator:
cos(0.6807) ≈ 0.7659
Work = 731.8266 N × 63.3 m × 0.7659
Work ≈ 35592.8 J
Therefore, the work required to pull the skier 63.3 m up a 39.0° slope at a constant speed of 2.0 m/s is approximately 35592.8 Joules.
To calculate the work required to pull the skier up the slope, we can use the equation:
Work = Force x Distance
In this case, the force required to move the skier up the slope is equal to the weight of the skier. The weight is given by:
Weight = mass x gravity
where mass is the mass of the skier and gravity is the acceleration due to gravity.
The distance moved up the slope is given as 63.3 m.
First, let's calculate the weight of the skier:
Weight = 74.6 kg x 9.81 m/s^2 (acceleration due to gravity)
Weight = 731.8266 N
Next, we can calculate the work required:
Work = Force x Distance
Work = 731.8266 N x 63.3 m
Work = 46,277.1758 J
Therefore, the work required to pull the skier up the slope is 46,277.1758 Joules.