Calculate Work Required for a 71 kg Skier on a 30° Slope with Constant Velocity

[bearhug]

A skier of mass 71 kg is pulled up a slope by a motor-driven cable.
(a) How much work is required to pull him a distance of 55 m up a 30° slope at a constant speed of 1.1 m/s

I'm having trouble trying to figure out where velocity comes into play here. Originally I was using the equation W=Fcosø ∆r and I found F using F=mgsinø. But my homework says this is wrong so I'm begging someone to help me out here.
Thanks

 

[Hootenanny]

You can answer this question one of two ways;

(1)Reslove the forces and find the tension in the cable, then multiply by the distance traveled up the slope.

(2)Find the work done against gravity (W = mgh).

 

[kyle8921]

To calculate the work required for the skier, we first need to understand the forces acting on the skier. The skier is being pulled up the slope by the motor-driven cable, which is providing a constant force in the direction of motion. This force can be found using the equation F=ma, where m is the mass of the skier and a is the acceleration, which is equal to 0 since the skier is moving at a constant velocity.

Next, we need to find the component of this force that is acting in the direction of motion. This can be done using the equation Fcosø, where ø is the angle of the slope, which in this case is 30°. So the force acting in the direction of motion is Fcos30°.

Now, the work required can be calculated using the equation W=Fd, where F is the force and d is the distance traveled. In this case, the distance traveled is 55 m and the force acting in the direction of motion is Fcos30°. So the work required is W=(Fcos30°)(55 m).

Substituting F=ma and solving for W, we get W=(ma)cos30°(55 m). Since the skier is moving at a constant velocity, we can use the equation a=v/t, where v is the velocity (1.1 m/s) and t is the time taken to travel the distance (55 m). So W=(m(1.1 m/s)/t)cos30°(55 m).

Now, we need to find the time taken to travel the distance. We can use the equation d=vavg x t, where d is the distance, vavg is the average velocity, and t is the time taken. In this case, vavg is equal to the velocity, since the skier is moving at a constant speed. So t=d/vavg=55 m/1.1 m/s=50 s.

Substituting this value of t in the equation for work, we get W=(m(1.1 m/s)/50 s)cos30°(55 m). Plugging in the given mass of 71 kg, we get W=(71 kg)(1.1 m/s)/50 s)cos30°(55 m)=93.1 J.

Therefore, the work required to pull the 71 kg skier a distance of 55 m up a 30