You are given a hydraulic jack which you'd like to keep in your car in case you have a flat. Your vehicle weighs 4500lbs, and you know the jack will have to lift 1500 lbs when you put it under the axle. The hand end cylinder of the jack is 1/2inch in diameter and the "work" end of the cylinder is 3.5 inches in diameter. It has an 8 inch long handle; the distance from the attachment point of the handle to the small piston of the jack is 1.5 inches. How much force will you have to apply to the end of the handle to lift the car and change a tire?
Force= 1500*/(MAjack*MaHandle)
Force= 1500/[(3.5/.5)^2 *(6.5/1.5)]
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check that
i don't understand that formula can you elaborate a little bit i came out with 7.07lbs of force and i don't think that is enough. Thanks
Car A has a speed of 20 km/h, which is being increased at the rate of 300 km/h2 as the car enters an expressway. At the same instant, car B is decelerating at 250 km/h2 while traveling forward at 100 km/h. Determine the velocity and acceleration of A with respect to B.
To understand the formula for calculating the force required to lift the car using the hydraulic jack, we need to look at the principle of Pascal's law and the concept of mechanical advantage.
Pascal's law states that when pressure is applied to a fluid in a confined space, the pressure is transmitted equally in all directions. In the case of a hydraulic jack, the fluid is usually oil or another type of hydraulic fluid.
The mechanical advantage (MA) of a hydraulic jack is the ratio of the cross-sectional area of the piston on the "work" end (the larger cylinder) to the cross-sectional area of the piston on the hand end (the smaller cylinder). In this case, the MA is determined by the ratio of the diameter squared of the larger cylinder to the diameter squared of the smaller cylinder.
The force equation for a hydraulic jack is given by:
Force = (Force_applied_to_small_piston) / (MA_jack * MA_handle)
Now let's calculate the force required to lift the car using the given information.
1. Calculate the mechanical advantage (MA_jack):
MA_jack = (diameter_work_end)^2 / (diameter_small_end)^2 = (3.5/2)^2 / (0.5/2)^2 = (12.25/0.25) = 49
2. Calculate the mechanical advantage of the handle (MA_handle):
MA_handle = length_of_handle / distance_from_handle_attachment_to_small_piston
MA_handle = 8 / 1.5 = 5.33
3. Substitute the values into the force equation:
Force = 1500 / (MA_jack * MA_handle)
Force = 1500 / (49 * 5.33)
Force ≈ 5.63 lbs
Therefore, the force required to lift the car using the hydraulic jack and change a tire is approximately 5.63 lbs.
As for the question about the velocity and acceleration of car A with respect to car B, we can use the concept of relative motion.
The velocity of car A with respect to car B can be calculated by subtracting the velocity of car B from the velocity of car A.
Velocity_A_B = Velocity_A - Velocity_B
Velocity_A_B = 20 km/h - (-100 km/h) = 120 km/h
So, car A is moving 120 km/h faster than car B.
The acceleration of car A with respect to car B can be calculated by subtracting the deceleration of car B from the acceleration of car A.
Acceleration_A_B = Acceleration_A - (-250 km/h^2)
Acceleration_A_B = 300 km/h^2 - (-250 km/h^2) = 550 km/h^2
Therefore, with respect to car B, car A has a velocity of 120 km/h and an acceleration of 550 km/h^2.