Gravity Work & Power of a Lawn Mower & Motion of a Cart

[kingsrock783]

Homework Statement

1a) Find the work done by the force of gravity.
Given- Force = 350 Newtons
distance = 2.00
1b) find the power of a lawn mower the time is 30 min and the force is 88 Newtons and the distance is 1.2 km

2a) a 15 kg cart starts from rest, travels 10 meters with a force of 105 Newtons. what is the final velocity?

2b) What is the carts work while pushing down the aisle
2c) what is the carts final kinetic energy?

Homework Equations

P= w/t , KE= 1/2mv^2, w=Fdcos(beta)

The Attempt at a Solution

 

[rock.freak667]

Your attempt at a solution is where now? We can't help you if you don't try

 

[ogb p]

1a) The work done by the force of gravity can be calculated using the formula W= Fd cos(beta), where F is the force of gravity, d is the distance, and beta is the angle between the force and the displacement. In this case, since the force of gravity is acting vertically downwards and the displacement is also in the same direction, the angle beta is 0 degrees. Therefore, the work done would be W= (350 N)(2.00 m)cos(0) = 700 Joules.

1b) The power of the lawn mower can be calculated using the formula P= W/t, where W is the work done, and t is the time. In this case, the work done would be W= (88 N)(1.2 km)cos(0) = 105.6 kJ. Converting the time from 30 minutes to seconds, we get t= 1800 seconds. Therefore, the power would be P= (105.6 kJ)/(1800 s) = 58.7 watts.

2a) The final velocity can be calculated using the formula v^2= u^2 + 2as, where u is the initial velocity (which is 0 since the cart starts from rest), a is the acceleration, and s is the distance traveled. Rearranging the formula, we get v= √(2as). Plugging in the given values, we get v= √(2(105 N)(10 m)/15 kg) = 7 m/s.

2b) The work done by the cart while pushing down the aisle can be calculated using the formula W= Fd cos(beta), where F is the force applied, d is the distance traveled, and beta is the angle between the force and displacement. In this case, since the force is acting in the same direction as the displacement, the angle beta is 0 degrees. Therefore, the work done would be W= (105 N)(10 m)cos(0) = 1050 Joules.

2c) The final kinetic energy can be calculated using the formula KE= 1/2mv^2, where m is the mass and v is the final velocity. Plugging in the given values, we get KE= 1/2(15 kg)(7 m/s)^2 = 367.5 Joules.