a man uses a roqe to haul box of weight 600N up an inclined wooden plank of effective lenght 3.0m and onto a platforn 1.0m high if indoing so, he exerts a force of 400N on the rope calculate (1) the frictional force between the case and the plank (2) the velocity ratio of the machine; (3) the mechanical advantage (4) theuseful workdone in joulesa man uses a roqe to haul box of weight 600N up an inclined wooden plank of effective lenght 3.0m and onto a platforn 1.0m high if indoing so, he exerts a force of 400N on the rope calculate (1) the frictional force between the case and the plank (2) the velocity ratio of the machine; (3) the mechanical advantage (4) theuseful workdone in joules?
I don't know the answer
triangle 1, up
3 hypotenuse, along plank
sqrt (8) = 2 sqrt 2, horizontal
plankward component of weight = 600 [ (2/3) sqrt 2] = 566 N
slopeward component of weight = 600 (1/3) = 200 N
(1) but we pulled with 400 N so friction force = 400-200 = 200 N
(2) velocity up/ velocity along slope = 1/3
(3) pulls with 400 and lifts 600 so 6/4 = 3/2
(4) 600 N * 1 meter up = 600 Joules
(1) The frictional force between the case and the plank would depend on the angle of the incline. Unfortunately, the angle is not mentioned in the question, so I can't provide a numerical answer. However, I can tell you that friction is no laughing matter! It always likes to make things difficult, just like that one person who borrows your pen and "forgets" to return it.
(2) To calculate the velocity ratio of the machine, you need the distance moved by the effort and the distance moved by the load. From the information provided, we know that the effective length of the plank is 3.0m and the platform is 1.0m high. But we don't have the distance moved by the effort or the load, so the velocity ratio is a mystery, just like how your socks mysteriously disappear in the washing machine.
(3) The mechanical advantage is the ratio of the load to the effort. In this case, the effort is 400N, but the weight of the box is given as 600N. However, the mechanical advantage would depend on the angle of the incline, which is not provided. So, without knowing the angle, I'm afraid the mechanical advantage remains a secret, just like the formula for turning lead into gold.
(4) The useful work done is calculated by multiplying the force exerted by the distance moved in the direction of force. With a force of 400N exerted on the rope, and the distance moved isn't given, so the calculation of useful work done is another unsolved puzzle, just like trying to find Waldo in a Where's Waldo book.
I hope these humorous responses bring a smile to your face, even if I couldn't provide the numerical answers you were looking for!
To answer the given questions, we need to use some basic principles of mechanics and work. Let's go step by step:
1) To find the frictional force between the case and the plank, we need to first calculate the force component parallel to the inclined plane, which is opposing the motion. This force is given by the equation:
Frictional force = force_parallel = force_applied - force_gravity_parallel
The force applied is stated as 400N, and the force of gravity parallel to the inclined plane can be calculated using trigonometry. The force of gravity parallel to the inclined plane is given by:
Force_gravity_parallel = weight * sin(theta)
where theta is the angle of inclination of the wooden plank. Assuming the angle is not given in the question, we cannot directly calculate the frictional force without this information.
2) The velocity ratio of the machine can be calculated by comparing the distance the rope is pulled to the vertical distance the load is lifted. The formula for velocity ratio is:
Velocity ratio = distance_pulled / vertical_distance_lifted
In this case, the distance pulled is 3.0m (the effective length of the plank) and the vertical distance lifted is 1.0m (the height of the platform). Plugging these values into the equation, we get:
Velocity ratio = 3.0 / 1.0 = 3.0
3) The mechanical advantage of the machine can be determined by comparing the force applied to the force obtained. The formula for mechanical advantage is:
Mechanical advantage = force_obtained / force_applied
In this case, the force obtained is the weight of the box, which is given as 600N, and the force applied is 400N. Plugging these values into the equation, we get:
Mechanical advantage = 600 / 400 = 1.5
4) The useful work done in joules can be calculated using the formula:
Useful work done = force_applied * distance_pulled * cosine(theta)
However, since the angle of inclination is not given in the question, we don't have enough information to calculate the useful work done.
In summary:
1) The frictional force cannot be calculated without knowing the angle of inclination.
2) The velocity ratio of the machine is 3.0.
3) The mechanical advantage of the machine is 1.5.
4) The useful work done in joules cannot be calculated without knowing the angle of inclination.