A compound machine is sued to lift a car. If you apply a force of 60 N to the machine, it lifts the car with a force of 550 N.
2 answers:
Answer:
a) 9.167
b) 402.5 J
Explanation:
We have a machine, which when applying a force of 60N, it returns 550N.
a) The mechanical advantage of a machine is the number of times that the machine increases an input force.
Mathematically, is the relationship between the output force and the input force.
The mechanical advantage is dimensionless.
In this case, the input force (the force we apply) is 60 N; and the output force (the force that the compound machine exerts) is 550 N.
We solve it this way:
This is the mechanical advantage of the machine in this exercise.
b)In a machine, we define the efficiency as the relationship between the work we receive from the machine, and the work we give to it.
The machine efficiency is a real number between 0 and 1 and is dimensionless.
In this exercise, the efficiency is 35% = 0.35
We solve it this way :
We obtain 402.5 J useful work from the machine.
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To solve for force, you need to get the product of mass and acceleration.
F = ma
Your given is:
m = 150g
a = ?
v = 50 m/s
t = 20ms
As you can see, you do not have acceleration yet. But if you read the problem you can come up with the formula of acceleration.
Acceleration is the change in velocity over a period of time.
a = change in velocity/time
To get the change in velocity, you get the difference between the initial velocity and final velocity:
The ball was moving initially at a velocity of 50 m/s and it came to a stop. This is your clue. If a ball comes to a stop then that means that the final velocity of the ball is 0 m/s.
So we can put it into our formula now:
WAIT! As you can see, the units do not match. We have ms and s into our equation and that means you cannot proceed till they are the same. First we need to convert ms to s.
x 
= 
So your new time is 0.02s. Now we put this time into the formula:
As you can see our acceleration is a negative value, this indicates that it decelerated or slowed down which makes sense because it was brought to a stop.
So now we have our acceleration. Now using this, we can get our force.
Before we start doing this, you need to take note that the unit of force is N, but when you expand it, it is
but as you can see our mass given is in grams. So again, before you put them into the equation we need to change it into kg first.
Our new mass is 0.150kg.
To make things clearer, let us write down all our new values:
m = 0.150kg
a = -2,500
Now that all our units match, we can put that into our formula:
The value again is negative because it is going against the initial direction of the ball. But if your instructor just wants to get the value of force or the magnitude of the force, just disregard the sign.
F = ma
Your given is:
m = 150g
a = ?
v = 50 m/s
t = 20ms
As you can see, you do not have acceleration yet. But if you read the problem you can come up with the formula of acceleration.
Acceleration is the change in velocity over a period of time.
a = change in velocity/time
To get the change in velocity, you get the difference between the initial velocity and final velocity:
The ball was moving initially at a velocity of 50 m/s and it came to a stop. This is your clue. If a ball comes to a stop then that means that the final velocity of the ball is 0 m/s.
So we can put it into our formula now:
WAIT! As you can see, the units do not match. We have ms and s into our equation and that means you cannot proceed till they are the same. First we need to convert ms to s.
So your new time is 0.02s. Now we put this time into the formula:
As you can see our acceleration is a negative value, this indicates that it decelerated or slowed down which makes sense because it was brought to a stop.
So now we have our acceleration. Now using this, we can get our force.
Before we start doing this, you need to take note that the unit of force is N, but when you expand it, it is
Our new mass is 0.150kg.
To make things clearer, let us write down all our new values:
m = 0.150kg
a = -2,500
Now that all our units match, we can put that into our formula:
The value again is negative because it is going against the initial direction of the ball. But if your instructor just wants to get the value of force or the magnitude of the force, just disregard the sign.