A skier of mass 70 kg is pulled up a slope by a motor-driven cable. (a) How much work is required to pull him 60m up a 30 degree slope (assumed frictionless) at a constant speed of 2.0 m/s? (b) What power must a motor have to perform this task?

he changes height by 60 sin30

work= mgh
power= mgh/T= mg d*sin30/T= mgv/2

I keep getting a number that is very large for (a). Is mg 70kg * 9.81?

Yes, the expression of Joules is generally very large when dealing with human beings moving slow, or small projectiles moving fast.

To calculate the work required to pull the skier up the slope, we need to consider the change in gravitational potential energy.

(a) To find the work done, we can use the formula:

Work = force * distance * cos(theta)

In this case, the force is the component of the gravitational force parallel to the slope, which is given by:

force = mass * acceleration due to gravity * sin(theta),

where theta is the angle of the slope. In this case, theta is 30 degrees.

The distance is given as 60m.

The skier is moving at a constant speed of 2.0 m/s, which means the net force on the skier is zero. So the force we calculated earlier, due to the slope, must be balanced by an equal and opposite force from the motor-driven cable.

Since the skier is moving at a constant speed, the net force is zero, and the force from the cable must be equal in magnitude but opposite in direction to the force due to the slope. Therefore, we can use the same force we calculated earlier for the slope.

Now, substituting the values into the equation:

Work = force * distance * cos(theta)
= (mass * acceleration due to gravity * sin(theta)) * distance * cos(theta)

Plugging in the values:
mass = 70 kg
acceleration due to gravity = 9.8 m/s^2
theta = 30 degrees
distance = 60m

Work = (70 kg * 9.8 m/s^2 * sin(30 degrees)) * 60m * cos(30 degrees)

Now we can calculate the work.

(b) To find the power required by the motor to perform this task, we can use the formula:

Power = work / time

Since the distance and speed are given, we can calculate the time as distance / speed.

Substituting the values into the equation:

Power = Work / (distance / speed)
= Work * speed / distance

Now, we can calculate the power.