a father pulls his young daughter on a sled with a constant velocity on a level surface through a distance of 10-m, if the total mass of the sled a the girl is 35-kg and the coefficent of kinetic friction between the sled runners and the snow is 0.20, how much work does the father do? the angle is 30 deg
To find the work done by the father, we need to calculate the force exerted by the father and the displacement experienced by the sled and the girl. The work done is given by the formula:
Work = Force * Displacement * cos(θ)
Where:
Force = Normal force - Frictional force
Displacement = Distance
θ = Angle between the force and the displacement
First, let's find the normal force acting on the sled and the girl. The normal force is equal to the weight of the sled and the girl. The weight can be calculated using the formula:
Weight = Mass * Gravity
Given:
Mass (m) = 35 kg
Gravity (g) = 9.8 m/s^2 (acceleration due to gravity)
Weight = 35 kg * 9.8 m/s^2
Weight = 343 N
Since the sled and the girl are moving with constant velocity, the net force acting on it is zero. This means the force of friction (F_friction) is equal in magnitude to the force exerted by the father (F_force), but in the opposite direction.
F_friction = μ * Normal force
Where:
μ = Coefficient of kinetic friction = 0.20
F_friction = 0.20 * 343 N
F_friction = 68.6 N
Now, let's calculate the force exerted by the father (F_force). Since the force exerted by the father is opposing the force of friction, we can write:
F_friction = -F_force
Therefore:
F_force = - F_friction
F_force = - 68.6 N
Next, we need to find the component of the force exerted by the father in the direction of displacement. This can be done using trigonometry. The angle between the force and the displacement is given as 30 degrees.
Force_component = F_force * cos(θ)
Force_component = - 68.6 N * cos(30°)
Finally, we can calculate the work done by the father:
Work = Force_component * Distance
Work = (- 68.6 N * cos(30°)) * 10 m
Using a calculator, we can find:
Work = - 594.82 J
Therefore, the work done by the father is approximately -594.82 Joules (J). The negative sign indicates that the force of the father is opposite to the direction of displacement.
To determine the work done by the father, we need to calculate the net force acting on the sled and the girl. Work is defined as the product of force and displacement.
First, let's calculate the normal force. Since the sled and the girl are on a level surface, the normal force is equal to the weight of the sled and the girl.
The weight is given by the formula: weight = mass * gravitational acceleration.
Assuming the gravitational acceleration is approximately 9.8 m/s^2, the weight of the sled and the girl is:
weight = 35 kg * 9.8 m/s^2 = 343 N.
The normal force is equal to the weight, so the normal force is also 343 N.
To find the net force acting on the sled and the girl, we need to subtract the force of friction from the applied force (the force exerted by the father).
The force of friction can be calculated using the formula: force of friction = coefficient of friction * normal force.
In this case, the coefficient of kinetic friction is 0.20, and the normal force is 343 N. Therefore, the force of friction is:
force of friction = 0.20 * 343 N = 68.6 N.
Since the sled and the girl are moving with a constant velocity, the net force must be zero. So, the force applied by the father is equal in magnitude but opposite in direction to the force of friction.
Therefore, the force applied by the father is 68.6 N, acting in the forward direction.
Now, we can calculate the work done by the father. The formula for work is:
work = force * displacement * cosine(angle between force and displacement).
Since the force applied by the father and the displacement are in the same direction, the angle between them is 0 degrees. The cosine of 0 degrees is 1, so we can omit that term.
Finally, the work done by the father is:
work = 68.6 N * 10 m = 686 J.
Therefore, the father does 686 Joules of work in pulling his daughter on the sled.
I don't see how "the angle" can be 30 degrees if the surface is level. Are you talking about the angle that his pulling force vector makes with the horizontal?
In any case, the work done on a level surface is the friction force times the distance that the sled is pulled (10 m). Use the coefficient of kinetic friction to get the friction force, Ff, using the equation.
Ff = (0.20) M g