Need help Newtons laws two diemnsions (vertical plane)

[flawlessbrown]

Homework Statement

A gardener pushes down on the handle of a lawnmover, applying a force of 250N. The handle is inclined at an angle 45* to the horizontal. If the coefficient of the kinetic friction between the wheels of the lawnmower and the ground is 0.40, what is the acceleration of the 20-kg lawnmower?

Homework Equations

Fnet=0=Fn+Fsin45-Fg
Fn=mg-FSin45
a=(Fx-Ff)/m
Fnet=ma
Ff=(UkFn) Uk=coefficient of friction miew? or meiu

The Attempt at a Solution

Answer is 1.38m/s^2

 

[PhanthomJay]

Your first equation applies on the y direction, but you have a signage error. The weight acts down and so does the vertical component of the applied force. The normal force acts up ; solve for it. Also, be sure to identify the horizontal component of the applied force, Fx.

 

[flawlessbrown]

Your first equation applies on the y direction, but you have a signage error. The weight acts down and so does the vertical component of the applied force. The normal force acts up ; solve for it. Also, be sure to identify the horizontal component of the applied force, Fx.

so are you saying my expression should be Fn= -mg+Fsin45 ?

 

[PhanthomJay]

You must be very careful with plus and minus signs, or else they will get the better of you. . Draw a free body diagram of the mower. The weight acts down on it, the vertical component of the applied force on the handle acts down on it, and the normal force of the ground acts up on it (normal contact forces are generally 'pushing' forces). Choose the up direction as positive and the down direction as negative. The algebraic sum of these three forces in the y direction must equal zero. Watch plus and minus signs, and solve for N.

 

[Nickie]

It seems like you have set up the equations correctly to solve for the acceleration of the lawnmower. The first step would be to calculate the normal force (Fn) acting on the lawnmower. This can be found by using the equation Fn=mg-Fsin45, where m is the mass of the lawnmower (20kg) and g is the acceleration due to gravity (9.8m/s^2). This gives us a value of Fn=138.6N.

Next, we can calculate the frictional force (Ff) acting on the lawnmower. This can be found using the equation Ff=UkFn, where Uk is the coefficient of kinetic friction (0.40) and Fn is the normal force we just calculated. This gives us a value of Ff=55.44N.

Now, we can use the equation Fnet=ma to find the acceleration of the lawnmower. We know that the net force acting on the lawnmower is the force applied by the gardener (250N) minus the frictional force (55.44N). So, we can set up the equation as follows:

Fnet=ma
250N-55.44N=20kg*a
194.56N=20kg*a

Solving for a, we get a=9.73m/s^2. However, this is the acceleration in the horizontal direction, and we are interested in the vertical acceleration. Using trigonometry, we can calculate the vertical component of this acceleration by multiplying it by the sine of the angle of inclination (45°). This gives us a vertical acceleration of 6.88m/s^2.

Therefore, the acceleration of the lawnmower in the vertical plane is 6.88m/s^2. I hope this helps with your homework! Remember to always double check your units and make sure they are consistent throughout your calculations.