A man uses a lever jack to lift a 2.00 × 10^3 kg car to change a tire. Each stroke of the jack lifts the car a distance of 5.00 × 10^(-3) m. The vertical displacement of the handle is 0.75 m for each stroke. How much total force does he use with each stroke of the jack?
A. 3.0 x 10^5 N
B. 2.9 x 10^6 N
C. 131 N
D. 19,600 N
weight = 2 * 10^3 * 9.81 = 19.62*10^3 N
mechanical advantage = .75/.005
= 150
(19.62/150)* 10^3 = 130.8 N
Well, let's break this down. The total force the man is using can be calculated using the formula:
Force = mass x acceleration
The mass of the car is given as 2.00 x 10^3 kg. Now, let's find the acceleration. We know that the car is being lifted a distance of 5.00 x 10^(-3) m each stroke and that the vertical displacement of the handle is 0.75 m.
To find the acceleration, we need to calculate the ratio of the distance the car is lifted to the distance the handle is displaced:
acceleration = (distance lifted) / (distance handle is displaced)
acceleration = (5.00 x 10^(-3)) / (0.75)
Simplifying this, we get:
acceleration = 6.67 x 10^(-3)
Now, let's substitute the values into the force formula:
Force = mass x acceleration
Force = (2.00 x 10^3) x (6.67 x 10^(-3))
Calculating this, we get:
Force = 13.34 N
Hmm, that doesn't match any of the answer choices. I think the correct answer must be option E: None of the above.
To find the total force used with each stroke of the jack, we can use the concept of work. Work is defined as the force applied on an object multiplied by the displacement of the object in the direction of the force. Mathematically, work (W) is given by the equation:
W = F × d,
where W is the work done, F is the force applied, and d is the displacement of the object.
In this case, the force we want to find is the force used with each stroke of the jack. The displacement is given as 5.00 × 10^(-3) m. We also know that the vertical displacement of the handle is 0.75 m for each stroke. Therefore, we can set up the following equation:
W = F × (0.75 m).
Since the car is lifted vertically, the work done on the car will be equal to the work done by the force applied by the man.
Therefore, the work done on the car can be calculated using the work-energy principle:
W = ΔPE,
where W is the work done, ΔPE is the change in potential energy of the car.
The potential energy of an object is given by the equation:
PE = m × g × h,
where m is the mass of the object, g is the acceleration due to gravity, and h is the vertical height.
In this case, the change in potential energy can be calculated as:
ΔPE = m × g × (0.75 m).
Since the work done on the car is equal to the change in potential energy, we can equate the two equations:
F × (0.75 m) = m × g × (0.75 m).
We can now solve for F.
F = (m × g × (0.75 m)) / (0.75 m).
Plugging in the given values:
F = (2.00 × 10^3 kg × 9.81 m/s^2 × (0.75 m)) / (0.75 m).
F = 2.00 × 10^3 kg × 9.81 m/s^2.
F = 19,620 N.
Therefore, the total force used with each stroke of the jack is approximately 19,600 N (option D).
To find the total force used with each stroke of the jack, we need to consider the mechanical advantage of the lever jack. The lever jack multiplies the force applied to the handle by a factor equal to the ratio of the distance the handle moves to the distance the car moves.
First, let's calculate the mechanical advantage (MA) of the jack. The formula for mechanical advantage is given by:
MA = distance moved by handle / distance moved by car
In this case, the distance moved by the handle is given as 0.75 m, and the distance moved by the car is given as 5.00 × 10^(-3) m.
MA = 0.75 m / (5.00 × 10^(-3) m)
MA = 150
The mechanical advantage of the lever jack is 150.
Next, we can calculate the force applied by the man with each stroke of the jack using the formula:
Force applied = weight of the car / mechanical advantage
The weight of the car is given as 2.00 × 10^3 kg. The force applied would then be:
Force applied = (2.00 × 10^3 kg) / 150
Force applied = 13.33 N (to two decimal places)
Therefore, the total force used with each stroke of the jack is approximately 13.33 N.
However, none of the given answer choices match this value. It seems there might be an error in the question or the answer choices. Please double-check the information provided.