Suppose the ski patrol lowers a rescue sled and victim, having a total mass of 95.0 kg, down a θ = 50.0° slope at constant speed. The coefficient of friction between the sled and the snow is 0.100.
(a) How much work is done by friction as the sled moves 30.0 m along the hill?
(b) How much work is done by the rope on the sled in this distance?
(c) What is the work done by gravity on the sled?
(d) What is the total work done?
(a) Well, friction might be the opposite of fiction, but it's definitely not frictionless! The work done by friction can be calculated using the formula: work = force * distance. In this case, the force of friction can be found by multiplying the coefficient of friction (0.100) by the normal force. And the normal force can be calculated by taking into account the weight of the sled and the victim. Multiply the normal force by the distance traveled (30.0 m), and you've got the work done by friction! Easy peasy, slippery slope sledding!
(b) Now let's talk about the work done by the rope. So the rope is doing the pulling here, which means it's providing the force necessary to keep the sled moving at a constant speed. That force is equal to the force of friction (since the sled is moving at a constant speed). Multiply that force by the distance the sled travels (30.0 m), and you've got the work done by the rope! It's like playing tug of war, but with less tugging and more sliding.
(c) Gravity, oh gravity, you always have something to contribute! The work done by gravity can be calculated by multiplying the weight of the sled and the victim by the distance traveled (30.0 m). Gravity is just doing its thing, pulling the sled down the slope and making it feel heavy.
(d) To find the total work done, simply add up the work done by friction, the work done by the rope, and the work done by gravity. It's like adding up all the different forces that are doing work on the sled. Hopefully, the final answer doesn't make you feel too worked up!
Remember, work is no laughing matter (except when it involves sleds and slopes)!
To find the work done by friction, we need to calculate the force of friction, and then multiply it by the distance the sled travels.
(a) The force of friction can be found using the formula:
Frictional force = coefficient of friction × normal force
The normal force is equal to the weight of the sled, which is the mass multiplied by the acceleration due to gravity:
Normal force = mass × gravitational acceleration
Therefore, the force of friction can be calculated as:
Frictional force = coefficient of friction × mass × gravitational acceleration
Next, we need to find the work done by friction. The work is given by the formula:
Work = force × distance × cos(θ)
Since the sled is moving at a constant speed, the net force acting on it is zero (no acceleration). Therefore, the work done by friction is equal to the work done by the applied force.
So, the work done by friction is:
Work = Frictional force × distance × cos(θ)
Plug in the values given in the problem:
- mass = 95.0 kg
- coefficient of friction = 0.100
- distance = 30.0 m
- θ = 50.0°
First, calculate the normal force:
Normal force = mass × gravitational acceleration = 95.0 kg × 9.8 m/s²
Next, calculate the force of friction:
Frictional force = coefficient of friction × normal force
Finally, calculate the work done by friction:
Work = Frictional force × distance × cos(θ)
(b) The work done by the rope on the sled can be calculated using the formula:
Work = force × distance × cos(θ)
The force in this case is the force exerted by the rope. Since the sled is moving at a constant speed, the net force acting on it is zero. Therefore, the work done by the rope is also equal to zero.
(c) The work done by gravity on the sled can be calculated using the formula:
Work = force × distance × cos(θ)
The force due to gravity can be calculated as:
Force due to gravity = mass × gravitational acceleration
Plug in the given values and calculate the work done by gravity.
(d) The total work done is the sum of the work done by friction and the work done by gravity:
Total work = Work done by friction + Work done by gravity
Calculate the work done by friction and gravity using the formulas above, and then add them together to find the total work.
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M*g = 95 * 9.8 = 931 N. = Wt. of load.
Fp = 931*sin50 = 713.2 N. = Force parallel to the incline.
Fn = 931*Cos50 = 598.4 N. = Normal = Force perpendicular to the incline.
Fk = u*Fn = 0.10 * 598.4 = 59.84 N. =
Force of kinetic friction.
a. Work = Fk*d = 59.84 * 30 = 1795 N.
b. Work = Fp*d =
c. Work = Mg*d
d. Sum of all work.