The formula for these....?

Question

I don't know the formula for these. Is there just one, or a different formula for each? Thanks!

1. A simple machine exerts a resistance force of 1,000 N when an effort force of 250 N is applied. What is the machine's mechanial advantage?

2. The effort force of 250 N includes a friction force of 50 N that must overcome. If there were no friction, what would the ideal mechanical advantage of this machine have been?

3. The work input to a machine is 25 J and the work output is 5 J. What is the efficiency of the machine?

4. An object moving a a speed of 1m/s has a kinetic energy of 5 J. What is its kinetic energy when it moves at 3m/s?

5. Suppose an object 10 m above the ground had a potential energy of 5 J. What will its potential energy be if it is raised to 20 m above the ground?

6. An object has a potential energy of 100 J when it is 10 m above the ground. If it were to fall without friction, what would its kinetic energy be the instant before it hit the ground?

Answer 1

1.
Mech Advantage= Force exerted / Force applied
Mech Advantage= 1,000/250 N = 4

2. 250/(250-50)=1.25

3. Efficiency = work out / work in
Eff= (5/25) x 100%=20%

4. Ke= 0.5 mV^2=

m= 2 Ke1/(V1^2)=2 Ke2/(V2^2)=
Ke2= [Ke1(V2/V1)^2=

Ke2 =5 (3/1)^2= 20J

5. Pe=mgh
mg=Pe1/h1=Pe2/h2
Pe2= Pe1(h2/h1)= 5 (20/10)=10J

6. Pe (initial)=Ke (final)